Academic Journal
A Simple and General Framework for the Construction of Thermodynamically Compatible Schemes for Computational Fluid and Solid Mechanics
| العنوان: | A Simple and General Framework for the Construction of Thermodynamically Compatible Schemes for Computational Fluid and Solid Mechanics |
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| المؤلفون: | Abgrall R., Busto S., Dumbser M. |
| المساهمون: | Abgrall, R., Busto, S., Dumbser, M. |
| سنة النشر: | 2023 |
| المجموعة: | Università degli Studi di Trento: CINECA IRIS |
| مصطلحات موضوعية: | hyperbolic and thermodynamically compatible (HTC) systems with extra conservation law, entropy inequality, Nonlinear stability in the energy norm, thermodynamically compatible finite volume scheme, thermodynamically compatible discontinuous Galerkin scheme, unified first order hyperbolic formulation of continuum mechanics |
| الوصف: | We introduce a simple and general framework for the construction of thermodynamically compatible schemes for the numerical solution of overdetermined hyperbolic PDE systems that satisfy an extra conservation law. As a particular example in this paper, we consider the general Godunov-Peshkov-Romenski (GPR) model of continuum mechanics that describes the dynamics of nonlinear solids and viscous fluids in one single unified mathematical formalism. A main peculiarity of the new algorithms presented in this manuscript is that the entropy inequality is solved as a primary evolution equation instead of the usual total energy conservation law, unlike in most traditional schemes for hyperbolic PDE. Instead, total energy conservation is obtained as a mere consequence of the proposed thermodynamically compatible discretization. The approach is based on the general framework introduced in Abgrall (2018) [1]. In order to show the universality of the concept proposed in this paper, we apply our new formalism to the construction of three different numerical methods. First, we construct a thermodynamically compatible finite volume (FV) scheme on collocated Cartesian grids, where discrete thermodynamic compatibility is achieved via an edge/face-based correction that makes the numerical flux thermodynamically compatible. Second, we design a first type of high order accurate and thermodynamically compatible discontinuous Galerkin (DG) schemes that employs the same edge/face-based numerical fluxes that were already used inside the finite volume schemes. And third, we introduce a second type of thermodynamically compatible DG schemes, in which thermodynamic compatibility is achieved via an element-wise correction, instead of the edge/face-based corrections that were used within the compatible numerical fluxes of the former two methods. All methods proposed in this paper can be proven to be nonlinearly stable in the energy norm and they all satisfy a discrete entropy inequality by construction. We present numerical results obtained ... |
| نوع الوثيقة: | article in journal/newspaper |
| اللغة: | English |
| Relation: | volume:440; issue:127629; firstpage:1; lastpage:40; numberofpages:40; journal:APPLIED MATHEMATICS AND COMPUTATION; https://hdl.handle.net/11572/360641; info:eu-repo/semantics/altIdentifier/scopus/2-s2.0-85139601771 |
| DOI: | 10.1016/j.amc.2022.127629 |
| الاتاحة: | https://hdl.handle.net/11572/360641 https://doi.org/10.1016/j.amc.2022.127629 |
| Rights: | info:eu-repo/semantics/openAccess |
| رقم الانضمام: | edsbas.F1D3A31 |
| قاعدة البيانات: | BASE |
| DOI: | 10.1016/j.amc.2022.127629 |
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