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Journal articles on the topic '2D Compressible Euler'

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Published: 11 March 2023

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1

Buckmaster, Tristan, and Sameer Iyer. "Formation of Unstable Shocks for 2D Isentropic Compressible Euler." Communications in Mathematical Physics 389, no. 1 (November 30, 2021): 197–271. http://dx.doi.org/10.1007/s00220-021-04271-z.

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2

Yuen, Manwai. "Vortical and self-similar flows of 2D compressible Euler equations." Communications in Nonlinear Science and Numerical Simulation 19, no. 7 (July 2014): 2172–80. http://dx.doi.org/10.1016/j.cnsns.2013.11.008.

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3

Zhang, Huali. "Local existence with low regularity for the 2D compressible Euler equations." Journal of Hyperbolic Differential Equations 18, no. 03 (September 2021): 701–28. http://dx.doi.org/10.1142/s0219891621500211.

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We prove the local existence, uniqueness and stability of local solutions for the Cauchy problem of two-dimensional compressible Euler equations, where the initial data of velocity, density, specific vorticity [Formula: see text] and the spatial derivative of specific vorticity [Formula: see text].

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4

Bressan, Alberto, Yi Jiang, and Hailiang Liu. "Numerical study of non-uniqueness for 2D compressible isentropic Euler equations." Journal of Computational Physics 445 (November 2021): 110588. http://dx.doi.org/10.1016/j.jcp.2021.110588.

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5

Godin, Paul. "The 2D compressible Euler equations in bounded impermeable domains with corners." Memoirs of the American Mathematical Society 269, no. 1313 (January 2021): 0. http://dx.doi.org/10.1090/memo/1313.

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6

Sun, Meina, and Chun Shen. "On the Riemann problem for 2D compressible Euler equations in three pieces." Nonlinear Analysis: Theory, Methods & Applications 70, no. 11 (June 2009): 3773–80. http://dx.doi.org/10.1016/j.na.2008.07.033.

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7

Baldauf, Michael. "Linear Stability Analysis of Runge–Kutta-Based Partial Time-Splitting Schemes for the Euler Equations." Monthly Weather Review 138, no. 12 (December 1, 2010): 4475–96. http://dx.doi.org/10.1175/2010mwr3355.1.

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Abstract For atmospheric simulation models with resolutions from about 10 km to the subkilometer cloud-resolving scale, the complete nonhydrostatic compressible Euler equations are often used. An important integration technique for them is the time-splitting (or split explicit) method. This article presents a comprehensive numerical stability analysis of Runge–Kutta (RK)-based partial time-splitting schemes. To this purpose a linearized two-dimensional (2D) compressible Euler system containing advection (as the slow process), sound, and gravity wave terms (as fast processes) is considered. These processes are the most important ones in limiting stability. First, the detailed stability properties are discussed with regard to several off-centering weights for each fast process described by horizontally explicit, vertically implicit schemes. Then the stability properties of the temporally and spatially discretized three-stage RK scheme for the complete 2D Euler equations and their stabilization (e.g., by divergence damping) are discussed. The main goal is to find optimal values for all of the occurring numerical parameters to guarantee stability in operational model applications. Furthermore, formal orders of temporal truncation errors for the time-splitting schemes are calculated. With the same methodology, two alternatives to the three-stage RK method, a so-called RK3-TVD method, and a new four-stage, second-order RK method are inspected.

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Arnold, Anton, and Ulrich Giering. "An Analysis of the Marshak Conditions for Matching Boltzmann and Euler Equations." Mathematical Models and Methods in Applied Sciences 07, no. 04 (June 1997): 557–77. http://dx.doi.org/10.1142/s0218202597000293.

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Domain decomposition methods based on matching the Boltzmann and Euler equations without overlapping are an important simulation technique in rarefied gas dynamics and semiconductor device modeling. Many existing codes use the Marshak boundary conditions (i.e. imposing continuity of the fluxes) at the interface between the two modeling regimes to implicitly determine the boundary data for the compressible Euler equations. In this paper we investigate the solvability of the Marshak conditions in the four different flow situations sub-/supersonic in-/outflow in one spacial dimension and for selected cases in 2D and 3D.

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9

Liu, Tiegang, A. W. Chowdhury, and Boo Cheong Khoo. "The Modified Ghost Fluid Method Applied to Fluid-Elastic Structure Interaction." Advances in Applied Mathematics and Mechanics 3, no. 5 (October 2011): 611–32. http://dx.doi.org/10.4208/aamm.10-m1054.

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AbstractIn this work, the modified ghost fluid method is developed to deal with 2D compressible fluid interacting with elastic solid in an Euler-Lagrange coupled system. In applying the modified Ghost Fluid Method to treat the fluid-elastic solid coupling, the Navier equations for elastic solid are cast into a system similar to the Euler equations but in Lagrangian coordinates. Furthermore, to take into account the influence of material deformation and nonlinear wave interaction at the interface, an Euler-Lagrange Riemann problem is constructed and solved approximately along the normal direction of the interface to predict the interfacial status and then define the ghost fluid and ghost solid states. Numerical tests are presented to verify the resultant method.

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10

Hou, Fei, and Huicheng Yin. "On global axisymmetric solutions to 2D compressible full Euler equations of Chaplygin gases." Discrete & Continuous Dynamical Systems - A 40, no. 3 (2020): 1435–92. http://dx.doi.org/10.3934/dcds.2020083.

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11

Tchuen, Ghislain, Pascalin Tiam Kapen, and Yves Burtschell. "An accurate shock-capturing scheme based on rotated-hybrid Riemann solver." International Journal of Numerical Methods for Heat & Fluid Flow 26, no. 5 (June 6, 2016): 1310–27. http://dx.doi.org/10.1108/hff-01-2015-0031.

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Purpose – The purpose of this paper is to present a new hybrid Euler flux fonction for use in a finite-volume Euler/Navier-Stokes code and adapted to compressible flow problems. Design/methodology/approach – The proposed scheme, called AUFSRR can be devised by combining the AUFS solver and the Roe solver, based on a rotated Riemann solver approach (Sun and Takayama, 2003; Ren, 2003). The upwind direction is determined by the velocity-difference vector and idea is to apply the AUFS solver in the direction normal to shocks to suppress carbuncle and the Roe solver across shear layers to avoid an excessive amount of dissipation. The resulting flux functions can be implemented in a very simple manner, in the form of the Roe solver with modified wave speeds, so that converting an existing AUFS flux code into the new fluxes is an extremely simple task. Findings – The proposed flux functions require about 18 per cent more CPU time than the Roe flux. Accuracy, efficiency and other essential features of AUFSRR scheme are evaluated by analyzing shock propagation behaviours for both the steady and unsteady compressible flows. This is demonstrated by several test cases (1D and 2D) with standard finite-volume Euler code, by comparing results with existing methods. Practical implications – The hybrid Euler flux function is used in a finite-volume Euler/Navier-Stokes code and adapted to compressible flow problems. Originality/value – The AUFSRR scheme is devised by combining the AUFS solver and the Roe solver, based on a rotated Riemann solver approach.

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12

QU, KUN, CHANG SHU, and YONG TIAN CHEW. "SIMULATION OF SHOCK-WAVE PROPAGATION WITH FINITE VOLUME LATTICE BOLTZMANN METHOD." International Journal of Modern Physics C 18, no. 04 (April 2007): 447–54. http://dx.doi.org/10.1142/s012918310701067x.

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A new approach was recently proposed to construct equilibrium distribution functions [Formula: see text] of the lattice Boltzmann method for simulation of compressible flows. In this approach, the Maxwellian function is replaced by a simple function which satisfies all needed relations to recover compressible Euler equations. With Lagrangian interpolation polynomials, the simple function is discretized onto a fixed velocity pattern to construct [Formula: see text]. In this paper, the finite volume method is combined with the new lattice Boltzmann models to simulate 1D and 2D shock-wave propagation. The numerical results agree well with available data in the literatures.

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13

Drikakis, D., and S. Tsangaris. "Real Gas Effects for Compressible Nozzle Flows." Journal of Fluids Engineering 115, no. 1 (March 1, 1993): 115–20. http://dx.doi.org/10.1115/1.2910092.

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Numerical simulation of compressible nozzle flows of real gas with or without the addition of heat is presented. A generalized real gas method, using an upwind scheme and curvilinear coordinates, is applied to solve the unsteady compressible Euler equations in axisymmetric form. The present method is an extension of a previous 2D method, which was developed to solve the problem for a gas having the general equation of state in the form p = p(ρ, i). In the present work the method is generalized for an arbitrary P-V-T equation of state introducing an iterative procedure for the determination of the temperature from the specific internal energy and the flow variables. The solution procedure is applied for the study of real gas effects in an axisymmetric nozzle flow.

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14

Guerra, Jorge E., and Paul A. Ullrich. "Spectral steady-state solutions to the 2D compressible Euler equations for cross-mountain flows." Communications in Applied Mathematics and Computational Science 16, no. 1 (June 22, 2021): 99–117. http://dx.doi.org/10.2140/camcos.2021.16.99.

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15

Glimm, James, Xiaomei Ji, Jiequan Li, Xiaolin Li, Peng Zhang, Tong Zhang, and Yuxi Zheng. "Transonic Shock Formation in a Rarefaction Riemann Problem for the 2D Compressible Euler Equations." SIAM Journal on Applied Mathematics 69, no. 3 (January 2008): 720–42. http://dx.doi.org/10.1137/07070632x.

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16

Wang, Li, and Dimitri J. Mavriplis. "Adjoint-based h–p adaptive discontinuous Galerkin methods for the 2D compressible Euler equations." Journal of Computational Physics 228, no. 20 (November 2009): 7643–61. http://dx.doi.org/10.1016/j.jcp.2009.07.012.

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17

Chen, Xi, Natalia Andronova, Bram Van Leer, Joyce E. Penner, John P. Boyd, Christiane Jablonowski, and Shian-Jiann Lin. "A Control-Volume Model of the Compressible Euler Equations with a Vertical Lagrangian Coordinate." Monthly Weather Review 141, no. 7 (July 1, 2013): 2526–44. http://dx.doi.org/10.1175/mwr-d-12-00129.1.

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Abstract Accurate and stable numerical discretization of the equations for the nonhydrostatic atmosphere is required, for example, to resolve interactions between clouds and aerosols in the atmosphere. Here the authors present a modification of the hydrostatic control-volume approach for solving the nonhydrostatic Euler equations with a Lagrangian vertical coordinate. A scheme with low numerical diffusion is achieved by introducing a low Mach number approximate Riemann solver (LMARS) for atmospheric flows. LMARS is a flexible way to ensure stability for finite-volume numerical schemes in both Eulerian and vertical Lagrangian configurations. This new approach is validated on test cases using a 2D (x–z) configuration.

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18

Hou, Fei, and Huicheng Yin. "Global smooth axisymmetric solutions to 2D compressible Euler equations of Chaplygin gases with non-zero vorticity." Journal of Differential Equations 267, no. 5 (August 2019): 3114–61. http://dx.doi.org/10.1016/j.jde.2019.03.038.

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19

Choquard, Ph, and M. Vuffray. "The inviscid, compressible and rotational, 2D isotropic Burgers and pressureless Euler–Coriolis fluids: Solvable models with illustrations." Physica D: Nonlinear Phenomena 285 (October 2014): 18–27. http://dx.doi.org/10.1016/j.physd.2014.06.010.

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20

Luk, Jonathan, and Jared Speck. "Shock formation in solutions to the 2D compressible Euler equations in the presence of non-zero vorticity." Inventiones mathematicae 214, no. 1 (June 18, 2018): 1–169. http://dx.doi.org/10.1007/s00222-018-0799-8.

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21

Zhang, Laiping, Ming Li, Wei Liu, and Xin He. "An Implicit Algorithm for High-Order DG/FV Schemes for Compressible Flows on 2D Arbitrary Grids." Communications in Computational Physics 17, no. 1 (December 19, 2014): 287–316. http://dx.doi.org/10.4208/cicp.091113.280714a.

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AbstractA Newton/LU-SGS (lower-upper symmetric Gauss-Seidel) iteration implicit method was developed to solve two-dimensional Euler and Navier-Stokes equations by the DG/FV hybrid schemes on arbitrary grids. The Newton iteration was employed to solve the nonlinear system, while the linear system was solved with LU-SGS iteration. The effect of several parameters in the implicit scheme, such as the CFL number, the Newton sub-iteration steps, and the update frequency of Jacobian matrix, was investigated to evaluate the performance of convergence history. Several typical test cases were simulated, and compared with the traditional explicit Runge-Kutta (RK) scheme. Firstly the Couette flow was tested to validate the order of accuracy of the present DG/FV hybrid schemes. Then a subsonic inviscid flow over a bump in a channel was simulated and the effect of parameters was investigated also. Finally, the implicit algorithm was applied to simulate a subsonic inviscid flow over a circular cylinder and the viscous flow in a square cavity. The numerical results demonstrated that the present implicit scheme can accelerate the convergence history efficiently. Choosing proper parameters would improve the efficiency of the implicit scheme. Moreover, in the same framework, the DG/FV hybrid schemes are more efficient than the same order DG schemes.

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22

Ma, Xinrong, Sanyang Liu, and Gongnan Xie. "Predictor-Corrector LU-SGS Discontinuous Galerkin Finite Element Method for Conservation Laws." Mathematical Problems in Engineering 2015 (2015): 1–11. http://dx.doi.org/10.1155/2015/940257.

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Efficient implicit predictor-corrector LU-SGS discontinuous Galerkin (DG) approach for compressible Euler equations on unstructured grids is investigated by adding the error compensation of high-order term. The original LU-SGS and GMRES schemes for DG method are discussed. Van Albada limiter is employed to make the scheme monotone. The numerical experiments performed for the transonic inviscid flows around NACA0012 airfoil, RAE2822 airfoil, and ONERA M6 wing indicate that the present algorithm has the advantages of low storage requirements and high convergence acceleration. The computational efficiency is close to that of GMRES scheme, nearly 2.1 times greater than that of LU-SGS scheme on unstructured grids for 2D cases, and almost 5.5 times greater than that of RK4 on unstructured grids for 3D cases.

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23

Marques, N. P. C., and J. C. F. Pereira. "Comparison of three second-order accurate reconstruction schemes for 2D Euler and Navier-Stokes compressible flows on unstructured grids." Communications in Numerical Methods in Engineering 17, no. 5 (April 3, 2001): 309–23. http://dx.doi.org/10.1002/cnm.408.

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24

Chakkour, Tarik. "Application of Two-dimensional Finite Volume Method to Protoplanetary Disks." International Journal of Mechanics 15 (October 20, 2021): 233–45. http://dx.doi.org/10.46300/9104.2021.15.27.

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Many fascinating astrophysical phenomena can be simulated insufficiently by standard numerical schemes for the compressible hydrodynamics equations. In the present work, a high performant 2D hydrodynamical code has been developed. The model is designed for the planetary formation that consists of momentum, continuity and energy equations. Since the two-phase model seems to be hardly executed, we will show in a simplified form, the implementation of this model in one-phase. It is applied to the Solar System that such stars can form planets. The finite volume method (FVM) is used in this model. We aim to develop a first-order well-balanced scheme for the Euler equations in the the radial direction, combined with second-order centered ux following the radial direction. This conception is devoted to balance the uxes, and guarantee hydrostatic equilibrium preserving. Then the model is used on simplified examples in order to show its ca- pability to maintain steady-state solutions with a good precision. Additionally, we demonstrate the performance of the numerical code through simulations. In particularly, the time evolution of gas orbited around the star, and some proper- ties of the Rossby wave instability are analyzed. The resulting scheme shows consequently that this model is robust and simple enough to be easily implemented.

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25

Loubère, Raphaël, Michael Dumbser, and Steven Diot. "A New Family of High Order Unstructured MOOD and ADER Finite Volume Schemes for Multidimensional Systems of Hyperbolic Conservation Laws." Communications in Computational Physics 16, no. 3 (September 2014): 718–63. http://dx.doi.org/10.4208/cicp.181113.140314a.

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AbstractIn this paper, we investigate the coupling of the Multi-dimensional Optimal Order Detection (MOOD) method and the Arbitrary high order DERivatives (ADER) approach in order to design a new high order accurate, robust and computationally efficient Finite Volume (FV) scheme dedicated to solve nonlinear systems of hyperbolic conservation laws on unstructured triangular and tetrahedral meshes in two and three space dimensions, respectively. The Multi-dimensional Optimal Order Detection (MOOD) method for 2D and 3D geometries has been introduced in a recent series of papers for mixed unstructured meshes. It is an arbitrary high-order accurate Finite Volume scheme in space, using polynomial reconstructions witha posterioridetection and polynomial degree decrementing processes to deal with shock waves and other discontinuities. In the following work, the time discretization is performed with an elegant and efficient one-step ADER procedure. Doing so, we retain the good properties of the MOOD scheme, that is to say the optimal high-order of accuracy is reached on smooth solutions, while spurious oscillations near singularities are prevented. The ADER technique permits not only to reduce the cost of the overall scheme as shown on a set of numerical tests in 2D and 3D, but it also increases the stability of the overall scheme. A systematic comparison between classical unstructured ADER-WENO schemes and the new ADER-MOOD approach has been carried out for high-order schemes in space and time in terms of cost, robustness, accuracy and efficiency. The main finding of this paper is that the combination of ADER with MOOD generally outperforms the one of ADER and WENO either because at given accuracy MOOD is less expensive (memory and/or CPU time), or because it is more accurate for a given grid resolution. A large suite of classical numerical test problems has been solved on unstructured meshes for three challenging multi-dimensional systems of conservation laws: the Euler equations of compressible gas dynamics, the classical equations of ideal magneto-Hydrodynamics (MHD) and finally the relativistic MHD equations (RMHD), which constitutes a particularly challenging nonlinear system of hyperbolic partial differential equation. All tests are run on genuinely unstructured grids composed of simplex elements.

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Sewerin, P., L. Dötsch, D. Truhm, D. Abrar, and S. Nebelung. "THU0062 FUNCTIONAL MR IMAGING OF HUMAN MENISCUS IS ASSOCIATED WITH HISTOLOGICAL DEGENERATION." Annals of the Rheumatic Diseases 79, Suppl 1 (June 2020): 243. http://dx.doi.org/10.1136/annrheumdis-2020-eular.6403.

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Background:In OA, there is a close association of meniscus and cartilage pathologies. Meniscus degeneration and lesioning are critical risk factors for development of early OA. Hence, thisex-vivostudy assessed the responses to standardized loading of human meniscus samples as a function of degeneration and based on changes in their T1, T2 and T1ρ maps (as surrogate parameters of the tissue’s functionality).Objectives:Can meniscus functionality be visualized by serial quantitative MRI mapping technics?Methods:During total knee replacements, 45 meniscus samples of variable degeneration were harvested from the center of the lateral meniscus body (Fig. 1a1-a3). After preparation to standard, samples were subject to force-controlled loading using an MRI-compatible lever device that created compressive loading by torque ((Fig. 1a4-a5). For each sample and loading position, MRI measurements (as detailed below) were performed in the unloaded (δ0) and loaded configurations, i.e. loaded to 2 bar (δ1, 37.1 N compressive force, 0.67 Nm torque) and to 4 bar (δ2, 69.1 N, 1.24 Nm). Throughout all loading positions, morphological and quantitative imaging was performed using Proton Density-weighted and T1, T1ρ, and T2 mapping sequences (3.0 T, Achieva, Philips) based on standard turbospin-echo, inversion-recovery, spin-lock multi-gradient-echo, and multi-spin-echo sequences. For reference purposes, histological (i.e. Pauli classification) and biomechanical measures (i.e. Elastic Modulus) were obtained for each sample. Based on Pauli sum scores, samples were trichotomized as grossly intact, (n=14), mildly degenerated (n=16), and moderate-to-severely degenerated (n=15).Figure 1.Preparation of meniscus samples and details of the MRI-compatible loading device. The lateral meniscus (a1) was cut to standard size by use of a dedicated cutting block (a2) to eventually obtain lateral meniscus samples (from the body region) of standard dimensions (a3). These samples were then placed in a dedicated MRI-compatible loading device for pressure-controlled, quasi-static and torque-induced loading under simultaneous MR imaging (a4). Two parallel support beams allowed standardized positioning in the MRI scanner‘s bore (a5).Results:Morphologically, loading induced deformation and flattening in all samples (Fig. 2a). For T1, homogeneous loading-induced decreases in all samples were found, irrespective of degeneration (Fig. 2b). For T1ρ, increases in the apical zones of intact samples were observed, and decreases in degenerated samples (Fig. 2c). For T2, changes were ambiguous and incoherent (Fig. 2d).Figure 2.Serial morphological images and functional maps of histologically moderately degenerative human meniscus as a function of force-controlled loading. Serial PDw (a), T1 (b), T1ρ (c), and T2 maps (d) are displayed at increasing loading intensity (δ0: unloaded [a1-d1]; δ1: loaded to 2 bar [a2-d2]; δ2: loaded to 4 bar [a3-d3]). Histologically, this sample demonstrated signs of severe surface desintegration and disruption. Pauli sum score 12, i.e. moderate to severe degeneration (Pauli Grade III). In b – d, color-coded parameter value maps are overlaid onto the corresponding morphological images. Histological sections are stained with Hematoxylin-Eosin (e1) and Safranin O (e2).Conclusion:Meniscus functionality may be visualized using serial quantitative MRI mapping techniques. T1ρ may provide an imaging biomarker of relevant intra-tissue adaptations that seem to be associated with histological degeneration. The perspective evaluation of meniscus functionality may be indicative of incipient or manifest load transmission failure to the adjacent cartilage layer.Disclosure of Interests:Philipp Sewerin Grant/research support from: AbbVie Deutschland GmbH & Co. KGBristol-Myers Squibb Celgene GmbHLilly Deutschland GmbHNovartis Pharma GmbH Pfizer Deutschland GmbHRheumazentrum Rhein-Ruhr, Consultant of: AMGEN GmbH AbbVie Deutschland GmbH & Co. KG Biogen GmbHBristol-Myers Squibb Celgene GmbH Chugai Pharma arketing Ltd. / Chugai Europe GmbHHexal Pharma Janssen-CilagGmbH Johnson & Johnson Deutschland GmbHLilly Deutschland GmbH / Lilly Europe / Lilly Global Novartis Pharma GmbH Pfizer Deutschland GmbH Roche Pharma Rheumazentrum Rhein-Ruhr Sanofi-Genzyme Deutschland GmbH Swedish Orphan Biovitrum GmbH UCB Pharma GmbH, Speakers bureau: AMGEN GmbH AbbVie Deutschland GmbH & Co. KG Biogen GmbHBristol-Myers Squibb Celgene GmbH Chugai Pharma arketing Ltd. / Chugai Europe GmbHHexal Pharma Janssen-CilagGmbH Johnson & Johnson Deutschland GmbHLilly Deutschland GmbH / Lilly Europe / Lilly Global Novartis Pharma GmbH Pfizer Deutschland GmbH Roche Pharma Rheumazentrum Rhein-Ruhr Sanofi-Genzyme Deutschland GmbH Swedish Orphan Biovitrum GmbH UCB Pharma GmbH, Lisa Dötsch: None declared, Daniel Truhm: None declared, Daniel Abrar: None declared, Sven Nebelung: None declared

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27

Buckmaster, Tristan, Steve Shkoller, and Vlad Vicol. "Formation of Shocks for 2D Isentropic Compressible Euler." Communications on Pure and Applied Mathematics, October 27, 2020. http://dx.doi.org/10.1002/cpa.21956.

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28

Wei, Feng, Liang Jin, Jun Liu, Feng Ding, and Xinping Zheng. "GPU acceleration of a 2D compressible Euler solver on CUDA-based block-structured Cartesian meshes." Journal of the Brazilian Society of Mechanical Sciences and Engineering 42, no. 5 (April 21, 2020). http://dx.doi.org/10.1007/s40430-020-02290-w.

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29

Mitra, Sourav. "Observability and unique continuation of the adjoint of a linearized simplified compressible fluid-structure model in a 2d channel." ESAIM: Control, Optimisation and Calculus of Variations, October 6, 2020. http://dx.doi.org/10.1051/cocv/2020065.

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We consider a compressible fluid structure interaction model in a 2D channel with a simplified expression of the net force acting on the structure appearing at the fluid boundary. Concerning the structure we will consider a damped Euler-Bernoulli beam located on a portion of the boundary. In the present article we establish an observability inequality for the adjoint of the linearized fluid structure interaction problem under consideration which in principle is equivalent with the null controllability of the linearized system. As a corollary of the derived observability inequality we also obtain a unique continuation property for the adjoint problem.

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30

Jaiman, Rajeev K., Manoj K. Parmar, and Pardha S. Gurugubelli. "Added Mass and Aeroelastic Stability of a Flexible Plate Interacting With Mean Flow in a Confined Channel." Journal of Applied Mechanics 81, no. 4 (September 23, 2013). http://dx.doi.org/10.1115/1.4025304.

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This work presents a review and theoretical study of the added-mass and aeroelastic instability exhibited by a linear elastic plate immersed in a mean flow. We first present a combined added-mass result for the model problem with a mean incompressible and compressible flow interacting with an elastic plate. Using the Euler–Bernoulli model for the plate and a 2D viscous potential flow model, a generalized closed-form expression of added-mass force has been derived for a flexible plate oscillating in fluid. A new compressibility correction factor is introduced in the incompressible added-mass force to account for the compressibility effects. We present a formulation for predicting the critical velocity for the onset of flapping instability. Our proposed new formulation considers tension effects explicitly due to viscous shear stress along the fluid-structure interface. In general, the tension effects are stabilizing in nature and become critical in problems involving low mass ratios. We further study the effects of the mass ratio and channel height on the aeroelastic instability using the linear stability analysis. It is observed that the proximity of the wall parallel to the plate affects the growth rate of the instability, however, these effects are less significant in comparison to the mass ratio or the tension effects in defining the instability. Finally, we conclude this paper with the validation of the theoretical results with experimental data presented in the literature.

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