首页|High-Order ADER Discontinuous Galerkin Schemes for a Symmetric Hyperbolic Model of Compressible Barotropic Two-Fluid Flows

High-Order ADER Discontinuous Galerkin Schemes for a Symmetric Hyperbolic Model of Compressible Barotropic Two-Fluid Flows

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This paper presents a high-order discontinuous Galerkin(DG)finite-element method to solve the barotropic version of the conservative symmetric hyperbolic and thermodynami-cally compatible(SHTC)model of compressible two-phase flow,introduced by Romenski et al.in[59,62],in multiple space dimensions.In the absence of algebraic source terms,the model is endowed with a curl constraint on the relative velocity field.In this paper,the hyperbolicity of the system is studied for the first time in the multidimensional case,show-ing that the original model is only weakly hyperbolic in multiple space dimensions.To restore the strong hyperbolicity,two different methodologies are used:(ⅰ)the explicit sym-metrization of the system,which can be achieved by adding terms that contain linear com-binations of the curl involution,similar to the Godunov-Powell terms in the MHD equa-tions;(ⅱ)the use of the hyperbolic generalized Lagrangian multiplier(GLM)curl-cleaning approach forwarded.The PDE system is solved using a high-order ADER-DG method with a posteriori subcell finite-volume limiter to deal with shock waves and the steep gradients in the volume fraction commonly appearing in the solutions of this type of model.To illus-trate the performance of the method,several different test cases and benchmark problems have been run,showing the high order of the scheme and the good agreement when com-pared to reference solutions computed with other well-known methods.

Compressible two-fluid flowsSymmetric hyperbolic and thermodynamically compatible(SHTC)systemsHyperbolic systems with curl involutionsHigh-order ADER discontinuous Galerkin(DG)schemes with subcell finite-volume limiterConservative form of hyperbolic mo

Laura Río-Martín、Michael Dumbser

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Department of Civil,Environmental and Mechanical Engineering,University of Trento,Via Mesiano 77,Trento 38123,Italy

Department of Information Engineering and Computer Science,University of Trento,via Sommarive 9,Povo,Trento 38123,Italy

2024

10.1007/s42967-023-00313-6

应用数学与计算数学学报
上海大学

应用数学与计算数学学报

影响因子：0.165
ISSN：1006-6330
年,卷(期)：2024.6(4)