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Journal articles on the topic 'Convection mathematics'

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Published: 4 June 2021

Last updated: 15 February 2022

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1

Afanas'eva, Nadyezhda M., Alexander G. Churbanov, and Petr N. Vabishchevich. "Unconditionally Monotone Schemes for Unsteady Convection-Diffusion Problems." Computational Methods in Applied Mathematics 13, no. 2 (April 1, 2013): 185–205. http://dx.doi.org/10.1515/cmam-2013-0002.

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Abstract. This paper deals with constructing monotone schemes of the second-order accuracy in space for transient convection-diffusion problems. They are based on a reformulation of the convective and diffusive transport terms using the convective terms in the divergent and nondivergent forms. The stability of the difference schemes is established in the uniform and L1 norm. For 2D problems, unconditionally monotone schemes of splitting with respect to spatial variables are developed. Unconditionally stable schemes for problems of convection-diffusion-reaction are proposed, too.

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2

LAROZE, D., J. MARTÍNEZ-MARDONES, and C. PÉREZ-GARCIA. "ROTATING CONVECTION IN A BINARY VISCOELASTIC LIQUID MIXTURE." International Journal of Bifurcation and Chaos 15, no. 10 (October 2005): 3329–36. http://dx.doi.org/10.1142/s0218127405013927.

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In this work we report theoretical and numerical results on convection in a viscoelastic binary mixture under rotation. Instability thresholds for stationary convection are calculated. We obtain explicit expressions of convective thresholds in terms of the control parameters of the system for oscillatory convection. Finally, we analyze the stabilizing effect of rotation on instability thresholds for aqueous DNA suspensions.

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3

Vabishchevich, Petr N. "Iterative Methods for Solving Convection-diffusion Problem." Computational Methods in Applied Mathematics 2, no. 4 (2002): 410–44. http://dx.doi.org/10.2478/cmam-2002-0023.

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AbstractTo obtain an approximate solution of the steady-state convectiondiffusion problem, it is necessary to solve the corresponding system of linear algebraic equations. The basic peculiarity of these LA systems is connected with the fact that they have non-symmetric matrices. We discuss the questions of approximate solution of 2D convection-diffusion problems on the basis of two- and three-level iterative methods. The general theory of iterative methods of solving grid equations is used to present the material of the paper. The basic problems of constructing grid approximations for steady-state convection-diffusion problems are considered. We start with the consideration of the Dirichlet problem for the differential equation with a convective term in the divergent, nondivergent, and skew-symmetric forms. Next, the corresponding grid problems are constructed. And, finally, iterative methods are used to solve approximately the above grid problems. Primary consideration is given to the study of the dependence of the number of iteration on the Peclet number, which is the ratio of the convective transport to the diffusive one.

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4

LIND, PEDRO G., SVEN TITZ, TILL KUHLBRODT, JOÃO A. M. CORTE-REAL, JÜRGEN KURTHS, JASON A. C. GALLAS, and ULRIKE FEUDEL. "COUPLED BISTABLE MAPS: A TOOL TO STUDY CONVECTION PARAMETERIZATION IN OCEAN MODELS." International Journal of Bifurcation and Chaos 14, no. 03 (March 2004): 999–1015. http://dx.doi.org/10.1142/s0218127404009648.

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We present a study of ocean convection parameterization based on a novel approach which includes both eddy diffusion and advection and consists of a two-dimensional lattice of bistable maps. This approach retains important features of usual grid models and allows to assess the relative roles of diffusion and advection in the spreading of convective cells. For large diffusion our model exhibits a phase transition from convective patterns to a homogeneous state over the entire lattice. In hysteresis experiments we find staircase behavior depending on stability thresholds of local convection patterns. This nonphysical behavior is suspected to induce spurious abrupt changes in the spreading of convection in ocean models. The final steady state of convective cells depends not only on the magnitude of the advective velocity but also on its direction, implying a possible bias in the development of convective patterns. Such bias points to the need for an appropriate choice of grid geometry in ocean modeling.

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5

Hewitt, D. R. "Vigorous convection in porous media." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 476, no. 2239 (July 2020): 20200111. http://dx.doi.org/10.1098/rspa.2020.0111.

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The problem of convection in a fluid-saturated porous medium is reviewed with a focus on ‘vigorous’ convective flow, when the driving buoyancy forces are large relative to any dissipative forces in the system. This limit of strong convection is applicable in numerous settings in geophysics and beyond, including geothermal circulation, thermohaline mixing in the subsurface and heat transport through the lithosphere. Its manifestations range from ‘black smoker’ chimneys at mid-ocean ridges to salt-desert patterns to astrological plumes, and it has received a great deal of recent attention because of its important role in the long-term stability of geologically sequestered CO 2 . In this review, the basic mathematical framework for convection in porous media governed by Darcy’s Law is outlined, and its validity and limitations discussed. The main focus of the review is split between ‘two-sided’ and ‘one-sided’ systems: the former mimics the classical Rayleigh–Bénard set-up of a cell heated from below and cooled from above, allowing for detailed examination of convective dynamics and fluxes; the latter involves convection from one boundary only, which evolves in time through a series of regimes. Both set-ups are reviewed, accounting for theoretical, numerical and experimental studies in each case, and studies that incorporate additional physical effects are discussed. Future research in this area and various associated modelling challenges are also discussed.

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6

MARTÍNEZ-MARDONES, J., R. TIEMANN, W. ZELLER, and C. PÉREZ-GARCÍA. "AMPLITUDE EQUATION IN POLYMERIC FLUID CONVECTION." International Journal of Bifurcation and Chaos 04, no. 05 (October 1994): 1347–51. http://dx.doi.org/10.1142/s0218127494001052.

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The convective instabilities in viscoelastic polymeric Oldroyd-B models are studied. First, the nonlinear analysis of the stationary and oscillatory convection is carried out. Then, in the scope of weak nonlinear analysis, the coefficients of the amplitude equations are evaluated, in order to be in condition to estimate the possible behavior of stationary patterns and also travelling and standing waves. The values of these coefficients are determined by means of analytical and numerical techniques for convection in polymeric fluids.

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7

Dalík, Josef, and Helena Růžičková. "An explicit modified method of characteristics for the one-dimensional nonstationary convection-diffusion problem with dominating convection." Applications of Mathematics 40, no. 5 (1995): 367–80. http://dx.doi.org/10.21136/am.1995.134300.

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8

Cawood, M. E., V. J. Ervin, W. J. Layton, and J. M. Maubach. "Adaptive defect correction methods for convection dominated, convection diffusion problems." Journal of Computational and Applied Mathematics 116, no. 1 (April 2000): 1–21. http://dx.doi.org/10.1016/s0377-0427(99)00278-2.

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9

De l’Isle, François, and Robert G. Owens. "Superconsistent collocation methods with applications to convection-dominated convection–diffusion equations." Journal of Computational and Applied Mathematics 391 (August 2021): 113367. http://dx.doi.org/10.1016/j.cam.2020.113367.

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10

Loper, David E., and Paul H. Roberts. "Mush-Chimney Convection." Studies in Applied Mathematics 106, no. 2 (February 2001): 187–227. http://dx.doi.org/10.1111/1467-9590.00165.

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11

Fowler, A. C. "Fast Thermoviscous Convection." Studies in Applied Mathematics 72, no. 3 (June 1985): 189–219. http://dx.doi.org/10.1002/sapm1985723189.

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12

Webb, Mark J., Adrian P. Lock, Christopher S. Bretherton, Sandrine Bony, Jason N. S. Cole, Abderrahmane Idelkadi, Sarah M. Kang, et al. "The impact of parametrized convection on cloud feedback." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 373, no. 2054 (November 13, 2015): 20140414. http://dx.doi.org/10.1098/rsta.2014.0414.

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We investigate the sensitivity of cloud feedbacks to the use of convective parametrizations by repeating the CMIP5/CFMIP-2 AMIP/AMIP + 4K uniform sea surface temperature perturbation experiments with 10 climate models which have had their convective parametrizations turned off. Previous studies have suggested that differences between parametrized convection schemes are a leading source of inter-model spread in cloud feedbacks. We find however that ‘ConvOff’ models with convection switched off have a similar overall range of cloud feedbacks compared with the standard configurations. Furthermore, applying a simple bias correction method to allow for differences in present-day global cloud radiative effects substantially reduces the differences between the cloud feedbacks with and without parametrized convection in the individual models. We conclude that, while parametrized convection influences the strength of the cloud feedbacks substantially in some models, other processes must also contribute substantially to the overall inter-model spread. The positive shortwave cloud feedbacks seen in the models in subtropical regimes associated with shallow clouds are still present in the ConvOff experiments. Inter-model spread in shortwave cloud feedback increases slightly in regimes associated with trade cumulus in the ConvOff experiments but is quite similar in the most stable subtropical regimes associated with stratocumulus clouds. Inter-model spread in longwave cloud feedbacks in strongly precipitating regions of the tropics is substantially reduced in the ConvOff experiments however, indicating a considerable local contribution from differences in the details of convective parametrizations. In both standard and ConvOff experiments, models with less mid-level cloud and less moist static energy near the top of the boundary layer tend to have more positive tropical cloud feedbacks. The role of non-convective processes in contributing to inter-model spread in cloud feedback is discussed.

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13

DIEHL, STEFAN. "A UNIQUENESS CONDITION FOR NONLINEAR CONVECTION-DIFFUSION EQUATIONS WITH DISCONTINUOUS COEFFICIENTS." Journal of Hyperbolic Differential Equations 06, no. 01 (March 2009): 127–59. http://dx.doi.org/10.1142/s0219891609001794.

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The paper focuses on the uniqueness issue for scalar convection-diffusion equations where both the convective flux and diffusion functions have a spatial discontinuity. An interface entropy condition is proposed at such a spatial discontinuity. It implies the Kružkov-type entropy condition presented by Karlsen et al. in 2003. They proved uniqueness when the convective flux function satisfies an additional "crossing condition". The crossing condition becomes redundant with the entropy condition proposed here. Thereby, more general flux functions are allowed. Another advantage of the entropy condition is its simple geometrical interpretation, which facilitates the construction of stationary solutions.

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14

Manapova, Aigul. "On the differentiation of the functional in distributed optimization problems with imperfect contact." Filomat 32, no. 3 (2018): 775–83. http://dx.doi.org/10.2298/fil1803775m.

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We investigate issues of numerical solving of optimal control problems for second order elliptic equations with non-self-adjoint operators - convection-diffusion problems. Control processes are described by semi-linear convection-diffusion equation with discontinuous data and solutions (states) subject to the boundary interface conditions of imperfect type (i.e., problems with a jump of the coefficients and the solution on the interface; the jump of the solution is proportional to the normal component of the flux). Controls are involved in the coefficients of diffusion and convective transfer. We prove differentiability and Lipshitz continuity of the cost functional, depending on a state of the system and a control. The calculation of the gradients uses the numerical solutions of direct problems for the state and adjoint problems.

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15

Hayat, T., M. Waqas, S. A. Shehzad, and A. Alsaedi. "Mixed Convection Radiative Flow of Maxwell Fluid Near a Stagnation Point with Convective Condition." Journal of Mechanics 29, no. 3 (January 29, 2013): 403–9. http://dx.doi.org/10.1017/jmech.2013.6.

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AbstractEffects of thermal radiation in mixed convection stagnation point flow over a moving surface subject to convective boundary conditions is addressed. Mathematical modeling is based upon constitutive equations of an incompressible Maxwell fluid. Nonlinear analysis is presented through implementation of homotopy analysis method. Numerical values of Local Nusselt number is computed and analyzed.

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16

Brenier, Yann. "Rearrangement, convection, convexity and entropy." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 371, no. 2005 (December 28, 2013): 20120343. http://dx.doi.org/10.1098/rsta.2012.0343.

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The concepts of convexity and entropy play a crucial role in the mathematical theory of hyperbolic systems of conservation laws. We show that they also play an important role in the mathematical analysis of convection theory, through the mathematical concept of rearrangement.

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17

Lawrence, Jino, and Vanav Kumar Alagarsamy. "Mathematical Modelling of MHD Natural Convection in a Linearly Heated Porous Cavity." Mathematical Modelling of Engineering Problems 8, no. 1 (February 28, 2021): 149–57. http://dx.doi.org/10.18280/mmep.080119.

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A linear increase in thermal boundaries towards the bottom of the porous cavity is considered for numerical flow analysis on MHD natural convection. The two-dimensional square shaped cavity is filled with the Cu-water nanofluid. The dimensionless equations are considered to interpret the fluid and heat flow inside the cavity with respect to the desired boundaries. The governing equations are solved using the finite difference techniques. The relevant dimensionless parameters used in the present study are Rayleigh number, Darcy number, solid volume fraction of the nanoparticles and Hartmann number to obtain the flow fields. Heatline flows picturization techniques involved in the study analyze the heat flow inside the cavity. As the Rayleigh number and Darcy number increases, an increase in streamlines flow velocity and convection heat transfer is observed. Convective heat transfer is interrupted by increasing the applied magnetic field effects. An improvement in the heat transfer is noticed by increasing the solid volume fraction of the particles.

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18

Jeon, Youngmok. "Analysis of the cell boundary element methods for convection dominated convection–diffusion equations." Journal of Computational and Applied Mathematics 234, no. 8 (August 2010): 2469–82. http://dx.doi.org/10.1016/j.cam.2010.03.014.

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19

Vabishchevich, P. N. "Monotone Schemes for Convection–Diffusion Problems with Convective Transport in Different Forms." Computational Mathematics and Mathematical Physics 61, no. 1 (January 2021): 90–102. http://dx.doi.org/10.1134/s0965542520120155.

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20

Roberts, A. J. "Planform evolution in convection–an embedded centre manifold." Journal of the Australian Mathematical Society. Series B. Applied Mathematics 34, no. 2 (October 1992): 174–98. http://dx.doi.org/10.1017/s0334270000008717.

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AbstractThe new motion of embedding a centre manifold in some higher-dimensional manifold leads to a practical approach to the rational low-dimensional approximation of a wide class of dynamical systems; it also provides a simple geometric picture for these approximations. In particular, I consider the problem of finding an approximate, but accurate, description of the evolution of a two-dimensional planform of convection. Inspired by a simple example, the straightforward adiabatic iteration is proposed to estimate an embedding manifold and arguments are presented for its effectiveness. Upon applying the procedure to a model convective planform problem I find that the resulting approximations perform remarkably well–much better than the traditional Swift-Hohenberg approximation for planform evolution.

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21

Goldstein, C. I. "Preconditioning convection dominated convection‐diffusion problems." International Journal of Numerical Methods for Heat & Fluid Flow 5, no. 2 (February 1995): 99–119. http://dx.doi.org/10.1108/eum0000000004059.

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22

Ptashnyk, M. "Pseudoparabolic equations with convection." IMA Journal of Applied Mathematics 72, no. 6 (August 16, 2007): 912–22. http://dx.doi.org/10.1093/imamat/hxm053.

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23

Clavero, Carmelo, Jose L. Gracia, Grigorii Shishkin, and Lidia Shishkina. "Numerical Experiments for a Singularly Perturbed Parabolic Problem with Degenerating Convective Term and Discontinuous Source." Computational Methods in Applied Mathematics 12, no. 2 (2012): 139–52. http://dx.doi.org/10.2478/cmam-2012-0014.

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Abstract A finite difference scheme on special piecewise-uniform grids condensing in the interior layer is constructed for a singularly perturbed parabolic convection-diffusion equation with a discontinuous right-hand side and a multiple degenerating convective term (the convective flux is directed into the domain). When constructing the scheme, monotone grid approximations, similar to those developed and justified earlier by authors for a problem with a simple degenerating convective term, are used. Using the known technique of numerical experiments on embedded meshes, it is numerically verified that the constructed scheme converges ε-uniformly in the maximum norm at the convergence rate close to one.

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24

Banerjee, M. B., R. G. Shandil, P. Lal, and V. Kanwar. "A Mathematical Theorem in Rotatory Thermohaline Convection." Journal of Mathematical Analysis and Applications 189, no. 2 (January 1995): 351–61. http://dx.doi.org/10.1006/jmaa.1995.1023.

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25

Nishiura, Yasumasa. "The central philosophical viewpoint/concept of "mathematics of the commons" as a promising direction of applied mathematics." Impact 2020, no. 4 (October 13, 2020): 9–11. http://dx.doi.org/10.21820/23987073.2020.4.9.

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Professor Emeritus Yasumasa Nishiura is a mathematician who has dedicated his career to understanding more about the profound impact mathematics has on the world around us. He worked as Research Director at the Alliance for Breakthrough between Mathematics and Sciences (ABMS) (2007–2016) in Japan where he was supporting research activities in mathematical science that highlights their potential for solving societal problems. Nishiura is working with a team of researchers based at the Advanced Institute for Materials Research (AIMR), Tohoku University in Japan where they are studying self-organisation patterns that naturally manifest without design but have rhythm in space and time, such as polymers, convection, slime molds, and chemical reactions, to help learn more about pattern dynamics.

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26

Song, Lina, Yanren Hou, and Haibiao Zheng. "A variational multiscale method based on bubble functions for convection-dominated convection–diffusion equation." Applied Mathematics and Computation 217, no. 5 (November 2010): 2226–37. http://dx.doi.org/10.1016/j.amc.2010.07.023.

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27

Iliescu, Traian, and Zhu Wang. "Variational multiscale proper orthogonal decomposition: Convection-dominated convection-diffusion-reaction equations." Mathematics of Computation 82, no. 283 (March 18, 2013): 1357–78. http://dx.doi.org/10.1090/s0025-5718-2013-02683-x.

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28

Hebeker, F. K., and Yu A. Kuznetsov. "Unsteady convection and convection-diffusion problems via direct overlapping domain decomposition methods." Numerical Methods for Partial Differential Equations 14, no. 3 (May 1998): 387–406. http://dx.doi.org/10.1002/(sici)1098-2426(199805)14:3<387::aid-num7>3.0.co;2-i.

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29

Rashidi, Mohammad M., Mohammad Ferdows, Amir Basiri Parsa, and Shirley Abelman. "MHD Natural Convection with Convective Surface Boundary Condition over a Flat Plate." Abstract and Applied Analysis 2014 (2014): 1–10. http://dx.doi.org/10.1155/2014/923487.

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We apply the one parameter continuous group method to investigate similarity solutions of magnetohydrodynamic (MHD) heat and mass transfer flow of a steady viscous incompressible fluid over a flat plate. By using the one parameter group method, similarity transformations and corresponding similarity representations are presented. A convective boundary condition is applied instead of the usual boundary conditions of constant surface temperature or constant heat flux. In addition it is assumed that viscosity, thermal conductivity, and concentration diffusivity vary linearly. Our study indicates that a similarity solution is possible if the convective heat transfer related to the hot fluid on the lower surface of the plate is directly proportional to(x-)-1/2wherex-is the distance from the leading edge of the solid surface. Numerical solutions of the ordinary differential equations are obtained by the Keller Box method for different values of the controlling parameters associated with the problem.

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30

Kröner, Dietmar, and Mirko Rokyta. "Error estimates for higher-order finite volume schemes for convection–diffusion problems." Journal of Numerical Mathematics 26, no. 1 (March 26, 2018): 35–62. http://dx.doi.org/10.1515/jnma-2016-1056.

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AbstractIt is still an open problem to provea priorierror estimates for finite volume schemes of higher order MUSCL type, including limiters, on unstructured meshes, which show some improvement compared to first order schemes. In this paper we use these higher order schemes for the discretization of convection dominated elliptic problems in a convex bounded domainΩin ℝ2and we can prove such kind of ana priorierror estimate. In the part of the estimate, which refers to the discretization of the convective term, we gainh1/2. Although the original problem is linear, the numerical problem becomes nonlinear, due to MUSCL type reconstruction/limiter technique.

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31

Anley, Eyaya Fekadie, and Zhoushun Zheng. "Finite Difference Approximation Method for a Space Fractional Convection–Diffusion Equation with Variable Coefficients." Symmetry 12, no. 3 (March 23, 2020): 485. http://dx.doi.org/10.3390/sym12030485.

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Space non-integer order convection–diffusion descriptions are generalized form of integer order convection–diffusion problems expressing super diffusive and convective transport processes. In this article, we propose finite difference approximation for space fractional convection–diffusion model having space variable coefficients on the given bounded domain over time and space. It is shown that the Crank–Nicolson difference scheme based on the right shifted Grünwald–Letnikov difference formula is unconditionally stable and it is also of second order consistency both in temporal and spatial terms with extrapolation to the limit approach. Numerical experiments are tested to verify the efficiency of our theoretical analysis and confirm order of convergence.

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32

Stein, Robert F. "Magneto-convection." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 370, no. 1970 (July 13, 2012): 3070–87. http://dx.doi.org/10.1098/rsta.2011.0533.

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Convection is the transport of energy by bulk mass motions. Magnetic fields alter convection via the Lorentz force, while convection moves the fields via the curl( v × B ) term in the induction equation. Recent ground-based and satellite telescopes have increased our knowledge of the solar magnetic fields on a wide range of spatial and temporal scales. Magneto-convection modelling has also greatly improved recently as computers become more powerful. Three-dimensional simulations with radiative transfer and non-ideal equations of state are being performed. Flux emergence from the convection zone through the visible surface (and into the chromosphere and corona) has been modelled. Local, convectively driven dynamo action has been studied. The alteration in the appearance of granules and the formation of pores and sunspots has been investigated. Magneto-convection calculations have improved our ability to interpret solar observations, especially the inversion of Stokes spectra to obtain the magnetic field and the use of helioseismology to determine the subsurface structure of the Sun.

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33

Cen, Zhongdi. "A hybrid difference scheme for a singularly perturbed convection-diffusion problem with discontinuous convection coefficient." Applied Mathematics and Computation 169, no. 1 (October 2005): 689–99. http://dx.doi.org/10.1016/j.amc.2004.08.051.

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34

MORTON, K. W., and I. J. SOBEY. "Discretization of a convection-diffusion equation." IMA Journal of Numerical Analysis 13, no. 1 (1993): 141–60. http://dx.doi.org/10.1093/imanum/13.1.141.

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35

Chainais-Hillairet, Claire, and Maxime Herda. "Large-time behaviour of a family of finite volume schemes for boundary-driven convection–diffusion equations." IMA Journal of Numerical Analysis 40, no. 4 (November 11, 2019): 2473–504. http://dx.doi.org/10.1093/imanum/drz037.

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Abstract We are interested in the large-time behaviour of solutions to finite volume discretizations of convection–diffusion equations or systems endowed with nonhomogeneous Dirichlet- and Neumann-type boundary conditions. Our results concern various linear and nonlinear models such as Fokker–Planck equations, porous media equations or drift–diffusion systems for semiconductors. For all of these models, some relative entropy principle is satisfied and implies exponential decay to the stationary state. In this paper we show that in the framework of finite volume schemes on orthogonal meshes, a large class of two-point monotone fluxes preserves this exponential decay of the discrete solution to the discrete steady state of the scheme. This includes for instance upwind and centred convections or Scharfetter–Gummel discretizations. We illustrate our theoretical results on several numerical test cases.

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36

Straughan, B. "Triply resonant penetrative convection." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 468, no. 2148 (August 22, 2012): 3804–23. http://dx.doi.org/10.1098/rspa.2012.0211.

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A thermal convection model is considered that consists of a layer of viscous incompressible fluid contained between two horizontal planes. Gravity is acting vertically downward, and the fluid has a density maximum in the active temperature range. A heat source/sink that varies with vertical height is imposed. It is shown that in this situation there are three possible (different) sub-layers that may induce convective overturning instability. The possibility of resonance between the motion in these layers is investigated. A region is discovered where a very sharp increase in Rayleigh number is observed. In addition to a linearized instability analysis, two global (unconditional) nonlinear stability thresholds are derived.

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37

Hadavand, Mahshid, and Antonio C. M. Sousa. "Simulation of Thermomagnetic Convection in a Cavity Using the Lattice Boltzmann Model." Journal of Applied Mathematics 2011 (2011): 1–14. http://dx.doi.org/10.1155/2011/538637.

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Thermomagnetic convection in a differentially heated square cavity with an infinitely long third dimension is numerically simulated using the single relaxation time lattice Boltzmann method (LBM). This problem is of considerable interest when dealing with cooling of microelectronic devices, in situations where natural convection does not meet the cooling requirements, and forced convection is not viable due to the difficulties associated with pumping a ferrofluid. Therefore, circulation is achieved by imposing a magnetic field, which is created and controlled by placing a dipole at the bottom of the enclosure. The magnitude of the magnetic force is controlled by changing the electrical current through the dipole. In this study, the effects of combined natural convection and magnetic convection, which is commonly known as “thermomagnetic convection,” are analysed in terms of the flow modes and heat transfer characteristics of a magnetic fluid.

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38

Borne, Sabine Le. "ℋ-matrices for Convection-diffusion Problems with Constant Convection." Computing 70, no. 3 (June 2003): 261–74. http://dx.doi.org/10.1007/s00607-003-1474-4.

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39

BÜRGER, R., and K. H. KARLSEN. "ON A DIFFUSIVELY CORRECTED KINEMATIC-WAVE TRAFFIC FLOW MODEL WITH CHANGING ROAD SURFACE CONDITIONS." Mathematical Models and Methods in Applied Sciences 13, no. 12 (December 2003): 1767–99. http://dx.doi.org/10.1142/s0218202503003112.

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The well-known Lighthill–Whitham–Richards kinematic traffic flow model for unidirectional flow on a single-lane highway is extended to include both abruptly changing road surface conditions and drivers' reaction time and anticipation length. The result is a strongly degenerate convection–diffusion equation, where the diffusion term, accounting for the drivers' behavior, is effective only where the local car density exceeds a critical value, and the convective flux function depends discontinuously on the location. It is shown that the validity of the proposed traffic model is supported by a recent mathematical well-posedness (existence and uniqueness) theory for quasilinear degenerate parabolic convection–diffusion equations with discontinuous coefficients.20,22 This theory includes a convergence proof for a monotone finite-difference scheme, which is used herein to simulate the traffic flow model for a variety of situations.

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40

BLENNERHASSETT, P. J., and ANDREW P. BASSOM. "Nonlinear high-wavenumber Bénard convection." IMA Journal of Applied Mathematics 52, no. 1 (1994): 51–77. http://dx.doi.org/10.1093/imamat/52.1.51.

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41

Kruse, Carola, and Matthias Maischak. "Convection Problems on Anisotropic Meshes." Computational Methods in Applied Mathematics 13, no. 1 (January 1, 2013): 55–78. http://dx.doi.org/10.1515/cmam-2012-0003.

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Abstract. The Galerkin and SDFEM methods are compared for a steady state convection problem. The theoretical part of this work deals with the development of approximation results for continuous solutions on the unit square containing an edge singularity. In the numerical part we verify those approximation results by considering continuous as well as discontinuous solutions to the transport problem on an annular domain with a singularity at the inner circle.

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42

Davies, E. B. "An Indefinite Convection-Diffusion Operator." LMS Journal of Computation and Mathematics 10 (2007): 288–306. http://dx.doi.org/10.1112/s1461157000001418.

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AbstractWe give a mathematically rigorous analysis which confirms the surprising results in a recent paper of Benilov, O‘Brien and Sazonov [J. Fluid Mech. 497 (2003) 201-224] about the spectrum of a highly singular non-self-adjoint operator that arises in a problem in fluid mechanics. We also show that the set of eigenvectors does not form a basis for the operator.

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43

BORCIA, RODICA, DOMNIC MERKT, and MICHAEL BESTEHORN. "CONVECTIVE PATTERNS IN LIQUID–VAPOR SYSTEMS WITH DIFFUSE INTERFACE." International Journal of Bifurcation and Chaos 16, no. 09 (September 2006): 2705–11. http://dx.doi.org/10.1142/s0218127406016379.

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Recently, we have developed a phase field model to describe Marangoni convection with evaporation in a compressible fluid of van der Waals type away from criticality [Eur. Phys. J. B44 (2005)]. Using this model, we report now 2D fully nonlinear simulations where we emphasize the influence of evaporation on convective patterns.

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44

Marušić-Paloka, Eduard, and Andrey L. Piatnitski. "Homogenization of a Nonlinear Convection-Diffusion Equation with Rapidly Oscillating Coefficients and Strong Convection." Journal of the London Mathematical Society 72, no. 2 (October 2005): 391–409. http://dx.doi.org/10.1112/s0024610705006824.

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45

Sengul, Taylan, and Shouhong Wang. "Pattern formation in Rayleigh–Bénard convection." Communications in Mathematical Sciences 11, no. 1 (2013): 315–43. http://dx.doi.org/10.4310/cms.2013.v11.n1.a10.

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46

Zhang, Yang. "AD–FDSD for convection–diffusion problems." Applied Mathematics and Computation 206, no. 1 (December 2008): 257–71. http://dx.doi.org/10.1016/j.amc.2008.02.025.

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47

Heinrichs, Wilhelm. "Defect Correction for Convection-Dominated Flow." SIAM Journal on Scientific Computing 17, no. 5 (September 1996): 1082–91. http://dx.doi.org/10.1137/s1064827593243736.

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48

Gilding, B. H., and R. Kersner. "Instantaneous shrinking in nonlinear diffusion-convection." Proceedings of the American Mathematical Society 109, no. 2 (February 1, 1990): 385. http://dx.doi.org/10.1090/s0002-9939-1990-1007496-9.

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49

Nishida, Takaaki, and Yoshiaki Teramoto. "Pattern formations in heat convection problems." Chinese Annals of Mathematics, Series B 30, no. 6 (September 25, 2009): 769–84. http://dx.doi.org/10.1007/s11401-009-0101-x.

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50

Umavathi, Jawali C., Hafiz Muhammad Ali, and Sapnali Limbaraj Patil. "Triple diffusive mixed convection flow in a duct using convective boundary conditions." Mathematical Methods in the Applied Sciences 43, no. 15 (June 30, 2020): 9223–44. http://dx.doi.org/10.1002/mma.6617.

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