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Consult the lists of relevant articles, books, theses, conference reports, and other scholarly sources on the topic 'First-order hyperbolic partial differential equations.'
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Journal articles on the topic "First-order hyperbolic partial differential equations":
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Cheema, T. A., M. S. A. Taj, and E. H. Twizell. "Third-order methods for first-order hyperbolic partial differential equations." Communications in Numerical Methods in Engineering 20, no. 1 (November 4, 2003): 31–41. http://dx.doi.org/10.1002/cnm.650.
Turo, Jan. "On some class of quasilinear hyperbolic systems of partial differential-functional equations of the first order." Czechoslovak Mathematical Journal 36, no. 2 (1986): 185–97. http://dx.doi.org/10.21136/cmj.1986.102083.
Tokibetov, Zh A., N. E. Bashar, and А. К. Pirmanova. "THE CAUCHY-DIRICHLET PROBLEM FOR A SYSTEM OF FIRST-ORDER EQUATIONS." BULLETIN Series of Physics & Mathematical Sciences 72, no. 4 (December 29, 2020): 68–72. http://dx.doi.org/10.51889/2020-4.1728-7901.10.
For a single second-order elliptic partial differential equation with sufficiently smooth coefficients, all classical boundary value problems that are correct for the Laplace equations are Fredholm. The formulation of classical boundary value problems for the laplace equation is dictated by physical applications. The simplest of the boundary value problems for the Laplace equation is the Dirichlet problem, which is reduced to the problem of the field of charges distributed on a certain surface. The Dirichlet problem for partial differential equations in space is usually called the Cauchy-Dirichlet problem. This work dedicated to systems of first-order partial differential equations of elliptic and hyperbolic types consisting of four equations with three unknown variables. An explicit solution of the CauchyDirichlet problem is constructed using the method of an exponential – differential operator. Giving a very simple example of the co-solution of the Cauchy problem for a second-order differential equation and the Cauchy problem for systems of first-order hyperbolic differential equations.
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Kamont, Z., and S. Kozieł. "First Order Partial Functional Differential Equations with Unbounded Delay." gmj 10, no. 3 (September 2003): 509–30. http://dx.doi.org/10.1515/gmj.2003.509.
Abstract The phase space for nonlinear hyperbolic functional differential equations with unbounded delay is constructed. The set of axioms for generalized solutions of initial problems is presented. A theorem on the existence and continuous dependence upon initial data is given. The Cauchy problem is transformed into a system of integral functional equations. The existence of solutions of this system is proved by the method of successive approximations and by using theorems on integral inequalities. Examples of phase spaces are given.
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Karafyllis, Iasson, and Miroslav Krstic. "On the relation of delay equations to first-order hyperbolic partial differential equations." ESAIM: Control, Optimisation and Calculus of Variations 20, no. 3 (June 13, 2014): 894–923. http://dx.doi.org/10.1051/cocv/2014001.
Verma, Anjali, and Ram Jiwari. "Cosine expansion based differential quadrature algorithm for numerical simulation of two dimensional hyperbolic equations with variable coefficients." International Journal of Numerical Methods for Heat & Fluid Flow 25, no. 7 (September 7, 2015): 1574–89. http://dx.doi.org/10.1108/hff-08-2014-0240.
Purpose – The purpose of this paper is to present the computational modeling of second-order two-dimensional nonlinear hyperbolic equations by using cosine expansion-based differential quadrature method (CDQM). Design/methodology/approach – The CDQM reduced the equations into a system of second-order differential equations. The obtained system is solved by RK4 method by converting into a system of first ordinary differential equations. Findings – The computed numerical results are compared with the results presented by other workers (Mohanty et al., 1996; Mohanty, 2004) and it is found that the present numerical technique gives better results than the others. Second, the proposed algorithm gives good accuracy by using very less grid point and less computation cost as comparison to other numerical methods such as finite difference methods, finite elements methods, etc. Originality/value – The author extends CDQM proposed in (Korkmaz and Dağ, 2009b) for two-dimensional nonlinear hyperbolic partial differential equations. This work is new for two-dimensional nonlinear hyperbolic partial differential equations.
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Hou, Lei, Pan Sun, Jun Jie Zhao, Lin Qiu, and Han Lin Li. "Evaluation of Coupled Rheological Equations." Applied Mechanics and Materials 433-435 (October 2013): 1943–46. http://dx.doi.org/10.4028/www.scientific.net/amm.433-435.1943.
Apart from the convergence of the first-order hyperbolic partial differential equations in rheological flow,this paper estimate the general behavior of the solution. By analyzing the coupled partial differential equations on a macroscopic scale the solution of free surface flow has been obtained. Its asymptotic estimate of the solution and super convergence are proposed in the internal boundary layer.
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Ashyralyev, A., A. Ashyralyyev, and B. Abdalmohammed. "On the hyperbolic type differential equation with time involution." BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS 109, no. 1 (March 30, 2023): 38–47. http://dx.doi.org/10.31489/2023m1/38-47.
In the present paper, the initial value problem for the hyperbolic type involutory in t second order linear partial differential equation is studied. The initial value problem for the fourth order partial differential equations equivalent to this problem is obtained. The stability estimates for the solution and its first and second order derivatives of this problem are established.
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Hou, Lei, Jun Jie Zhao, and Han Ling Li. "Finite Element Convergence Analysis of Two-Scale Non-Newtonian Flow Problems." Advanced Materials Research 718-720 (July 2013): 1723–28. http://dx.doi.org/10.4028/www.scientific.net/amr.718-720.1723.
The convergence of the first-order hyperbolic partial differential equations in non-Newton fluid is analyzed. This paper uses coupled partial differential equations (Cauchy fluid equations, P-T/T stress equation) on a macroscopic scale to simulate the free surface elements. It generates watershed by excessive tensile elements. The semi-discrete finite element method is used to solve these equations. These coupled nonlinear equations are approximated by linear equations. Its super convergence is proposed.
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Bainov, Drumi, Zdzisław Kamont, and Emil Minchev. "Periodic boundary value problem for impulsive hyperbolic partial differential equations of first order." Applied Mathematics and Computation 68, no. 2-3 (March 1995): 95–104. http://dx.doi.org/10.1016/0096-3003(94)00083-g.
You might also be interested in the extended bibliographies on the topic 'First-order hyperbolic partial differential equations' for particular source types:
This thesis develops two families of numerical methods, based upon rational approximations having distinct real poles, for solving first- and second-order parabolic/ hyperbolic partial differential equations. These methods are thirdand fourth-order accurate in space and time, and do not require the use of complex arithmetic. In these methods first- and second-order spatial derivatives are approximated by finite-difference approximations which produce systems of ordinary differential equations expressible in vector-matrix forms. Solutions of these systems satisfy recurrence relations which lead to the development of parallel algorithms suitable for computer architectures consisting of three or four processors. Finally, the methods are tested on advection, advection-diffusion and wave equations with constant coefficients.
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Strogies, Nikolai. "Optimization of nonsmooth first order hyperbolic systems." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät, 2016. http://dx.doi.org/10.18452/17633.
Wir betrachten Optimalsteuerungsprobleme, die von partiellen Differentialgleichungen beziehungsweise Variationsungleichungen mit Differentialoperatoren erster Ordnung abhängen. Wir führen die Reformulierung eines Tagebauplanungsproblems, das auf stetigen Funktionen beruht, ein. Das Resultat ist ein Optimalsteuerungsproblem für Viskositätslösungen einer Eikonalgleichung. Die Existenz von Lösungen dieses und bestimmter Hilfsprobleme, die von semilinearen PDG‘s mit künstlicher Viskosität abhängen, wird bewiesen, Stationaritätsbedingungen hergeleitet und ein schwaches Konsistenzresultat für stationäre Punkte präsentiert. Des Weiteren betrachten wir Optimalsteuerungsprobleme, die von stationären Variationsungleichungen erster Art mit linearen Differentialoperatoren erster Ordnung abhängen. Wir diskutieren Lösbarkeit und Stationaritätskonzepte für diese Probleme. Für letzteres vergleichen wir Ergebnisse, die entweder durch die Anwendung von Penalisierungs- und Regularisierungsansätzen direkt auf Ebene von Differentialoperatoren erster Ordnung oder als Grenzwertprozess von Stationaritätssystemen für viskositätsregularisierte Optimalsteuerungsprobleme unter passenden Annahmen erhalten werden. Um die Konsistenz von ursprünglichem und regularisierten Problemen zu sichern, wird ein bekanntes Ergebnis für Lösungen von VU’s mit degeneriertem Differentialoperator erweitert. In beiden Fällen ist die erhaltene Stationarität schwächer als W-stationarität. Die theoretischen Ergebnisse werden anhand numerischer Beispiele verifiziert. Wir erweitern diese Ergebnisse auf Optimalsteuerungsprobleme bezüglich zeitabhängiger VU’s mit Differentialoperatoren erster Ordnung. Hierfür wird die Existenz von Lösungen bewiesen und erneut ein Stationaritätssystem mit Hilfe verschwindender Viskositäten unter bestimmten Beschränktheitsannahmen hergeleitet. Die erhaltenen Ergebnisse werden anhand von numerischen Beispielen verifiziert. We consider problems of optimal control subject to partial differential equations and variational inequality problems with first order differential operators. We introduce a reformulation of an open pit mine planning problem that is based on continuous functions. The resulting formulation is a problem of optimal control subject to viscosity solutions of a partial differential equation of Eikonal Type. The existence of solutions to this problem and auxiliary problems of optimal control subject to regularized, semilinear PDE’s with artificial viscosity is proven. For the latter a first order optimality condition is established and a mild consistency result for the stationary points is proven. Further we study certain problems of optimal control subject to time-independent variational inequalities of the first kind with linear first order differential operators. We discuss solvability and stationarity concepts for such problems. In the latter case, we compare the results obtained by either utilizing penalization-regularization strategies directly on the first order level or considering the limit of systems for viscosity-regularized problems under suitable assumptions. To guarantee the consistency of the original and viscosity-regularized problems of optimal control, we extend known results for solutions to variational inequalities with degenerated differential operators. In both cases, the resulting stationarity concepts are weaker than W-stationarity. We validate the theoretical findings by numerical experiments for several examples. Finally, we extend the results from the time-independent to the case of problems of optimal control subject to VI’s with linear first order differential operators that are time-dependent. After establishing the existence of solutions to the problem of optimal control, a stationarity system is derived by a vanishing viscosity approach under certain boundedness assumptions and the theoretical findings are validated by numerical experiments.
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Postell, Floyd Vince. "High order finite difference methods." Diss., Georgia Institute of Technology, 1990. http://hdl.handle.net/1853/28876.
Smith, James. "Global time estimates for solutions to higher order strictly hyperbolic partial differential equations." Thesis, Imperial College London, 2006. http://hdl.handle.net/10044/1/1267.
In this thesis we consider the Cauchy problem for general higher order constant coefficient strictly hyperbolic PDEs with lower order terms and show how the behaviour of the characteristic roots determine the rate of decay in the associated Lp-Lq estimates. In particular, we show under what conditions the solution behaves like that of the standard wave equation, the wave equation with dissipation or the Klein-Gordon equation. We explain the various factors involved, such as the presence of multiple roots, the size of the sets of multiplicity and the order with which characteristics meet the real axis, yield different rates of decay. As an example, we show how the results obtained can be applied to the Fokker-Planck equation. In the second part, we derive Lp-Lq estimates for wave equations with a bounded time dependent coefficient. A classification of the oscillating behaviour of the coefficient is given and related to the estimate which can be obtained.
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Jurás, Martin. "Geometric Aspects of Second-Order Scalar Hyperbolic Partial Differential Equations in the Plane." DigitalCommons@USU, 1997. https://digitalcommons.usu.edu/etd/7139.
The purpose of this dissertation is to address various geometric aspects of second-order scalar hyperbolic partial differential equations in two independent variables and one dependent variable
F(x, y, u, u_x, u_y, u_xx, u_xy, u_yy )= 0 (1)
We find a characterization of hyperbolic Darboux integrable equations at level k (1) in terms of the vanishing of the generalized Laplace invariants and provide an invariant characterization of various cases in the Goursat general classification of hyperbolic Darboux integrable equations (1). In particular we give a contact invariant characterization of equations integrable by the methods of general and intermediate integrals. New relative invariants that control the existence of the first integrals of the characteristic Pfaffian systems are found and used to obtain an invariant characterization for the class of -Gordon equations. A notion of a hyperbolic Darboux system is introduced and we show by examples that the classical Laplace transformation is just a special case of a diffeomorphism of hyperbolic Darboux systems. We also construct new examples of homomorphisms between certain hyperbolic systems. We characterize Monge-Ampere equations and explicitly exhibit two invariants whose vanishing is a necessary and sufficient condition for the equation to be of the Monge-Ampere type. The solution to the inverse problem of the calculus of variations for hyperbolic equations (1) in terms of the generalized Laplace invariants is presented. We also obtain some partial results on symplectic conservation laws. We characterize, up to contact equivalence, some classical equations using the generalized Laplace invariants. These results contain characterizations of the wave, Liouville, Klein-Gordon, and certain types of Euler-Poisson equations.
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Pefferly, Robert J. "Finite difference approximations of second order quasi-linear elliptic and hyperbolic stochastic partial differential equations." Thesis, University of Edinburgh, 2001. http://hdl.handle.net/1842/11244.
This thesis covers topics such as finite difference schemes, mean-square convergence, modelling, and numerical approximations of second order quasi-linear stochastic partial differential equations (SPDE) driven by white noise in less than three space dimensions. The motivation for discussing and expanding these topics lies in their implications in such physical phenomena as signal and information flow, gravitational and electromagnetic fields, large scale weather systems, and macro-computer networks. Chapter 2 delves into the hyperbolic SPDE in one space and one time dimension. This is an important equation to such fields as signal processing, communications, and information theory where singularities propagate throughout space as a function of time. Chapter 3 discusses some concepts and implications of elliptic SPDE's driven by additive noise. These systems are key for understanding steady state phenomena. Chapter 4 presents some numerical work regarding elliptic SPDE's driven by multiplicative and general noise. These SPDE's are open topics in the theoretical literature, hence numerical work provides significant insight into the nature of the process. Chapter 5 presents some numerical work regarding quasi-geostrophic geophysical fluid dynamics involving stochastic noise and demonstrates how these systems can be represented as a combination of elliptic and hyperbolic components.
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Luo, BiYong. "Shooting method-based algorithms for solving control problems associated with second-order hyperbolic partial differential equations." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2001. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp05/NQ66358.pdf.
Haque, Md Z. "An adaptive finite element method for systems of second-order hyperbolic partial differential equations in one space dimension." Ann Arbor, Mich. : ProQuest, 2008. http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:3316356.
Thesis (Ph.D. in Computational and Applied Mathematics)--S.M.U. Title from PDF title page (viewed Mar. 16, 2009). Source: Dissertation Abstracts International, Volume: 69-08, Section: B Adviser: Peter K. Moore. Includes bibliographical references.
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Sroczinski, Matthias [Verfasser]. "Global existence and asymptotic decay for quasilinear second-order symmetric hyperbolic systems of partial differential equations occurring in the relativistic dynamics of dissipative fluids / Matthias Sroczinski." Konstanz : KOPS Universität Konstanz, 2019. http://d-nb.info/1184795460/34.
Yang, Lixiang. "Modeling Waves in Linear and Nonlinear Solids by First-Order Hyperbolic Differential Equations." The Ohio State University, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=osu1303846979.
Galaktionov, Victor A. Blow-up for higher-order parabolic, hyperbolic, dispersion and Schrödinger equations. Boca Raton: CRC Press, Taylor & Francis Group, 2015.
Kenig, Carlos E. Lectures on the energy critical nonlinear wave equation. Providence, Rhode Island: Published for the Conference Board of the Mathematical Sciences by the American Mathematical Society, with support from the National Science Foundation, 2015.
Sequeira, A., H. Beirão da Veiga, and V. A. Solonnikov. Recent advances in partial differential equations and applications: International conference in honor of Hugo Beirao de Veiga's 70th birthday, February 17-214, 2014, Levico Terme (Trento), Italy. Edited by Rădulescu, Vicenţiu D., 1958- editor. Providence, Rhode Island: American Mathematical Society, 2016.
Nahmod, Andrea R. Recent advances in harmonic analysis and partial differential equations: AMS special sessions, March 12-13, 2011, Statesboro, Georgia : the JAMI Conference, March 21-25, 2011, Baltimore, Maryland. Edited by American Mathematical Society and JAMI Conference (2011 : Baltimore, Md.). Providence, Rhode Island: American Mathematical Society, 2012.
Conference on Multi-scale and High-contrast PDE: from Modelling, to Mathematical Analysis, to Inversion (2011 Oxford, England). Multi-scale and high-contrast PDE: From modelling, to mathematical analysis, to inversion : Conference on Multi-scale and High-contrast PDE:from Modelling, to Mathematical Analysis, to Inversion, June 28-July 1, 2011, University of Oxford, United Kingdom. Edited by Ammari Habib, Capdeboscq Yves 1971-, and Kang Hyeonbae. Providence, R.I: American Mathematical Society, 2010.
Book chapters on the topic "First-order hyperbolic partial differential equations":
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Alinhac, Serge. "Nonlinear First Order Equations." In Hyperbolic Partial Differential Equations, 27–40. New York, NY: Springer New York, 2009. http://dx.doi.org/10.1007/978-0-387-87823-2_3.
Gilbert, J. Charles, and Patrick Joly. "Higher Order Time Stepping for Second Order Hyperbolic Problems and Optimal CFL Conditions." In Partial Differential Equations, 67–93. Dordrecht: Springer Netherlands, 2008. http://dx.doi.org/10.1007/978-1-4020-8758-5_4.
Novruzi, Arian. "Second-order parabolic and hyperbolic PDEs." In A Short Introduction to Partial Differential Equations, 139–58. Cham: Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-39524-6_8.
Wen, G. C. "Complex Analytic Method for Hyperbolic Equations of Second Order." In Complex Methods for Partial Differential Equations, 271–88. Boston, MA: Springer US, 1999. http://dx.doi.org/10.1007/978-1-4613-3291-6_17.
Obolashvili, Elena. "Hyperbolic and Plurihyperbolic Equations in Clifford Analysis." In Higher Order Partial Differential Equations in Clifford Analysis, 125–50. Boston, MA: Birkhäuser Boston, 2003. http://dx.doi.org/10.1007/978-1-4612-0015-4_3.
Georgoulis, Emmanuil H., Edward Hall, and Charalambos Makridakis. "Error Control for Discontinuous Galerkin Methods for First Order Hyperbolic Problems." In Recent Developments in Discontinuous Galerkin Finite Element Methods for Partial Differential Equations, 195–207. Cham: Springer International Publishing, 2013. http://dx.doi.org/10.1007/978-3-319-01818-8_8.
Mitropolskii, Yu, G. Khoma, and M. Gromyak. "Asymptotic Methods for the Second Order Partial Differential Equations of Hyperbolic Type." In Asymptotic Methods for Investigating Quasiwave Equations of Hyperbolic Type, 161–97. Dordrecht: Springer Netherlands, 1997. http://dx.doi.org/10.1007/978-94-011-5752-0_7.
Demchenko, Vladimir V. "High-Gradient Method for the Solution of First Order Hyperbolic Type Systems with Partial Differential Equations." In Smart Modeling for Engineering Systems, 78–90. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-06228-6_8.
Pastor, Manuel. "Discretization Techniques for Transient, Dynamic and Cyclic Problems in Geotechnical Engineering: First Order Hyperbolic Partial Differential Equations." In Mechanical Behaviour of Soils Under Environmentally Induced Cyclic Loads, 291–327. Vienna: Springer Vienna, 2012. http://dx.doi.org/10.1007/978-3-7091-1068-3_5.
Dacorogna, Bernard, and Paolo Marcellini. "First Order Equations." In Implicit Partial Differential Equations, 33–68. Boston, MA: Birkhäuser Boston, 1999. http://dx.doi.org/10.1007/978-1-4612-1562-2_2.
Conference papers on the topic "First-order hyperbolic partial differential equations":
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Siranosian, Antranik A., Miroslav Krstic, Andrey Smyshlyaev, and Matt Bement. "Gain Scheduling-Inspired Control for Nonlinear Partial Differential Equations." In ASME 2009 Dynamic Systems and Control Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/dscc2009-2532.
We present a control design method for nonlinear partial differential equations (PDEs) based on a combination of gain scheduling and backstepping theory for linear PDEs. A benchmark first-order hyperbolic system with a destabilizing in-domain nonlinearity is considered first. For this system a nonlinear feedback law based on gain scheduling is derived explicitly, and a statement of stability is presented for the closed-loop system. Control designs are then presented for a string and shear beam PDE, both with Kelvin-Voigt damping and potentially destabilizing free-end nonlinearities. String and beam simulation results illustrate the merits of the gain scheduling approach over the linearization-based design.
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Vatankhah, Ramin, Mohammad Abediny, Hoda Sadeghian, and Aria Alasty. "Backstepping Boundary Control for Unstable Second-Order Hyperbolic PDEs and Trajectory Tracking." In ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/detc2009-87038.
In this paper, a problem of boundary feedback stabilization of second order hyperbolic partial differential equations (PDEs) is considered. These equations serve as a model for physical phenomena such as oscillatory systems like strings and beams. The controllers are designed using a backstepping method, which has been recently developed for parabolic PDEs. With the integral transformation and boundary feedback the unstable PDE is converted into a system which is stable in sense of Lyapunov. Then taylorian expansion is used to achieve the goal of trajectory tracking. It means design a boundary controller such that output of the system follows an arbitrary map. The designs are illustrated with simulations.
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Freitas Rachid, Felipe Bastos. "A Numerical Model for Gaseous Cavitation Flow in Liquid Transmission Lines." In ASME 2006 2nd Joint U.S.-European Fluids Engineering Summer Meeting Collocated With the 14th International Conference on Nuclear Engineering. ASMEDC, 2006. http://dx.doi.org/10.1115/fedsm2006-98106.
This work presents a numerical model for predicting the isothermal transient two-phase flow of liquid-gas homogeneous mixtures in rigid pipelines. The resulting mathematical problem is governed by a system of non-linear hyperbolic partial differential equations which is solved by means of an operator splitting technique, combined with the Glimm’s method. To implement Glimm’s method, it is presented the closed-form analytical solution of the associated Riemann problem. Uniqueness of this solution is demonstrated for a general set of equations of state for the liquid and the gas. Preliminary numerical results are presented in order to illustrated the model performance.
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Figueiredo, Aline B., David E. G. P. Bueno, Renan M. Baptista, Felipe B. F. Rachid, and Gustavo C. R. Bodstein. "Accuracy Study of the Flux-Corrected Transport Numerical Method Applied to Transient Two-Phase Flow Simulations in Gas Pipelines." In 2012 9th International Pipeline Conference. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/ipc2012-90002.
The ability to produce accurate numerical simulations of transient two-phase flows in gas pipelines has long been an important issue in the oil industry. A reliable prediction of such flows is a difficult task to accomplish due to the numerous sources of uncertainties, such as the basic two-phase flow model, the flow-pattern models, the initial condition and the numerical method used to solve the system of partial differential equations. Several numerical methods, conservative or not, of first- and second-order accuracies may be used to discretize the problem. In this paper we use the flux-corrected transport (FCT) finite-difference method to solve a one-dimensional single-pressure four-equation two-fluid model for the two-phase flow that occurs in a nearly horizontal pipeline characterized by the stratified-flow pattern. Because the FCT algorithm is of indeterminate order, we use a test case to assess the spatial and time accuracies for the specific class of hyperbolic problem that we obtain with the modeling employed here. The results show that the method is first order in time and second order in space, which have important consequences on the choice of mesh spacing and time step for a desired accuracy.
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Farzin, Amir, Zahir Barahmand, and Bernt Lie. "Experimental PDE solver in Julia – comparison of flux limiting schemes." In 63rd International Conference of Scandinavian Simulation Society, SIMS 2022, Trondheim, Norway, September 20-21, 2022. Linköping University Electronic Press, 2022. http://dx.doi.org/10.3384/ecp192007.
Finite Volume Methods (FVM) are high quality methods for solving conservative/hyperbolic partial differential equations (PDEs). A popular class of high-resolution methods utilize a nonlinear combination of low order methods and high order methods via flux limiting functions. Another class of high-resolution methods is the class of weighted essentially non-oscillatory (WENO) schemes. Here, the focus is on flux limiting schemes. An experimental finite volume (FV) semi-discrete solver for systems of hyperbolic PDEs has been implemented in Julia, utilizing Julia’s DifferentialEquations.jl package for handling the time marching. A first order upwind formulation is used for the low order method, and a central second order formulation is used for the high order method. The PDE can be provided either in flux form, or in quasi-linear form. In the former case, automatic differentiation (AD) package ForwardDiff.jl is used to compute the Jacobians of the flux vector. Package LinearAlgebra.jl is used to compute the eigenspace of the Jacobians. The implementation allows for up to 3 internal/external coordinates. More than a dozen flux limiting functions are given, with the possibility of the users to write their own flux limiters. The implementation allows for user provided spatial discretization points, and source terms in the PDE. In this paper, we will compare various flux limiting schemes for PDEs with analytic solutions, and will also compare flux limiting schemes for a simple granulation model (layering). Possible extensions of the experimental implementation include: (i) higher order methods, (ii) more extensive support for boundary conditions, (iii) improved support for source terms.
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de Freitas, Raphael V. N., Carina N. Sondermann, Rodrigo A. C. Patricio, Aline B. Figueiredo, Gustavo C. R. Bodstein, Felipe B. F. Rachid, and Renan M. Baptista. "Numerical Study of Two-Phase Flow in a Horizontal Pipeline Using an Unconditionally Hyperbolic Two-Fluid Model." In ASME 2018 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/imece2018-87571.
Numerical simulation is a very useful tool for the prediction of physical quantities in two-phase flows. One important application is the study of oil-gas flows in pipelines, which is necessary for the proper selection of the equipment connected to the line during the pipeline design stage and also during the pipeline operation stage. The understanding of the phenomena present in this type of flow is more crucial under the occurrence of undesired effects in the duct, such as hydrate formation, fluid leakage, PIG passage, and valve shutdown. An efficient manner to model two-phase flows in long pipelines regarding a compromise between numerical accuracy and cost is the use of a one-dimensional two-fluid model, discretized with an appropriate numerical method. A two-fluid model consists of a system of non-linear partial differential equations that represent the mass, momentum and energy conservation principles, written for each phase. Depending on the two-fluid model employed, the system of equations may lose hyperbolicity and render the initial-boundary-value problem illposed. This paper uses an unconditionally hyperbolic two-fluid model for solving two-phase flows in pipelines in order to guarantee that the solution presents physical consistency. The mathematical model here referred to as the 5E2P (five equations and two pressures) comprises two equations of continuity and two momentum conservation equations, one for each phase, and one equation for the transport of the volume fraction. A priori this model considers two distinct pressures, one for each phase, and correlates them through a pressure relaxation procedure. This paper presents simulation cases for stratified two-phase flows in horizontal pipelines solved with the 5E2P coupled with the flux corrected transport method. The objective is to evaluate the numerical model capacity to adequately describe the velocities, pressures and volume fraction distributions along the duct.
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Jiménez, Edson M., Juan P. Escandón, and Oscar E. Bautista. "Study of the Transient Electroosmotic Flow of Maxwell Fluids in Square Cross-Section Microchannels." In ASME 2015 13th International Conference on Nanochannels, Microchannels, and Minichannels collocated with the ASME 2015 International Technical Conference and Exhibition on Packaging and Integration of Electronic and Photonic Microsystems. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/icnmm2015-48547.
Several kinds of fluids with non-Newtonian behavior are manipulated in microfluidic devices for medical, chemical and biological applications. This work presents an analytical solution for the transient electroosmotic flow of Maxwell fluids in square cross-section microchannels. The appropriate combination of the momentum equation with the rheological Maxwell model derives in a mathematical model based in a hyperbolic partial differential equation, that permits to determine the velocity profile. The flow field is solved using the Green’s functions for the steady-state regime, and the method of separation of variables for the transient phenomenon in the electroosmotic flow. Taking in to account the normalized form of the governing equations, we predict the influence of the main dimensionless parameters on the velocity profiles. The results show an oscillatory behavior in the transient stage of the fluid flow, which is directly controlled by the dimensionless relaxation time, this parameter is an indicator of the competition between elastic and viscous effects. Hence, this investigation about the characteristics of the fluid rheology on the fluid velocity of the transient electroosmotic flow are discussed in order to contribute to the understanding the different tasks and design of microfluidic devices.
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Catania, A. E., A. Ferrari, and M. Manno. "Acoustic Cavitation Thermodynamic Modeling in Transmission Pipelines by an Implicit Conservative High-Resolution Numerical Algorithm." In ASME 2006 2nd Joint U.S.-European Fluids Engineering Summer Meeting Collocated With the 14th International Conference on Nuclear Engineering. ASMEDC, 2006. http://dx.doi.org/10.1115/fedsm2006-98272.
A general treatment of acoustic cavitation for the case of one-dimensional pipe flows is presented, including both fluid dynamics instabilities, which can occur at cavitation inception, and non-equilibrium effects during bubble dynamics. Different approaches to cavitation modelling are also considered and compared. A novel barotropic cavitation model has been developed, based on the partial differential equations governing the mass conservation and momentum balance. The analytical expression for the vapour source term driving cavitation has been carried out by means of the energy conservation equation and a general formula for the sound speed in homogeneous bubbly flows has been used. A newly developed high-resolution, conservative, implicit, second-order accurate numerical scheme was applied to solve the Euler’s hyperbolic equations governing the pipe flow. It gave reduced oscillation problems at the discontinuities that were induced by cavitation. The resultant computational model was assessed through its application to a literature test-case, which involved a pipe connecting two constant-pressure reservoirs, water being the working fluid. The prediction outcomes were discussed so as to underline the most interesting fluid-dynamic phenomena, such as the dynamics of shock waves arising at cavitation collapse. The influence of the frequency-dependent friction model on the simulation of the pressure wave dynamics in the presence of cavitation was also analysed.
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Ferna´ndez, Manuel Rodri´guez, Evangelino Garrido Torres, and Ricardo Ortega Garci´a. "TrenSen: A New Way to Study the Unsteady Behaviour of Air Inside Tunnels—Application to High Speed Railway Lines." In ASME 2011 International Mechanical Engineering Congress and Exposition. ASMEDC, 2011. http://dx.doi.org/10.1115/imece2011-62641.
During the last decades, high speed railway traffic system has achieved a great development all over the world. Increasing speed in the train circulation implies the apparition of new aerodynamic phenomena that need to be studied. One of these problems has to do with the entrance and exit of high speed (HS) trains in tunnels. When this occurs, pressure waves propagate and reflect through the tunnel at sound speed, generating a non-stationary movement of the air which depends greatly on the speed of the train and the geometry between train and tunnel. A study has been carried on to determine the pressure and velocity fields of air inside the tunnel when the train passes through. As a result of this study, a new software, “TrenSen”, has been developed. This program solves numerically a particular case of the Navier-Stokes equations, a hyperbolic system of partial differential equations which describe the flow behaviour inside the tunnel. In the first section of the paper presented hereby a description of the algebra for the fluid dynamics equations is conducted. The second section will explain some features of the software, ending with some numerical results obtained from the program. To finish the paper, the software is validated by comparing the numeric results with available experimental data and with some other commercial software.
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Catania, Andrea E., Alessandro Ferrari, Michele Manno, and Ezio Spessa. "A Comprehensive Thermodynamic Approach to Acoustic Cavitation Simulation in High-Pressure Injection Systems by a Conservative Homogeneous Barotropic-Flow Model." In ASME 2003 Internal Combustion Engine and Rail Transportation Divisions Fall Technical Conference. ASMEDC, 2003. http://dx.doi.org/10.1115/icef2003-0760.
A general conservative numerical model for simulation of transmission-line unsteady fluid-dynamics has been developed and applied to high-pressure injection systems. A comprehensive thermodynamic approach for modeling acoustic cavitation, i.e. cavitation induced by wave propagation, was proposed on the basis of a homogeneous barotropic mixture model of a pure liquid in equilibrium with its vapor and a gas, both dissolved and undissolved. For the pure liquid flow simulation outside the cavitation regions, or in the absence of these, temperature variations due to compressibility effects were taken into account, for the first time in injection system simulation, through a thermodynamic state equation which was derived from energy considerations. Nevertheless, in the cavitation regions, an isothermal flow was retained which is consistent with negligible thermal effects due to vaporization because of the tiny amounts of liquid involved. A novel implicit, conservative, one step, symmetrical and trapezoidal scheme of the second-order accuracy was applied to solve the hyperbolic partial differential equations governing the pipe flows. It can also be enhanced at a high-resolution level. The numerical model was applied to wave propagation and cavitation simulation in a high-pressure injection system of the pump-line-nozzle type for light and medium duty vehicles. The system was of relevance to the model assessment because it presented severely cavitating flow conditions. The predicted pressure time histories at two pipe locations and injector needle lift were compared to experimental results, substantiating the validity and robustness of the developed conservative model in simulating cavitation inception and desinence with great degree of accuracy. Cavitation transients and the flow discontinuities induced by them were numerically analyzed and discussed.
Reports on the topic "First-order hyperbolic partial differential equations":
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Gottlieb, Sigal. High Order Strong Stability Preserving Time Discretizations for the Time Evolution of Hyperbolic Partial Differential Equations. Fort Belvoir, VA: Defense Technical Information Center, February 2012. http://dx.doi.org/10.21236/ada564549.
Cornea, Emil, Ralph Howard, and Per-Gunnar Martinsson. Solutions Near Singular Points to the Eikonal and Related First Order Non-linear Partial Differential Equations in Two Independent Variables. Fort Belvoir, VA: Defense Technical Information Center, March 2000. http://dx.doi.org/10.21236/ada640692.
