On the Use of Different Sets of Variables for Solving Unsteady Inviscid Flows with an Implicit Discontinuous Galerkin Method
This article presents a comparison between the performance obtained by using a spatial discretization of the Euler equations based on a high-order discontinuous Galerkin (dG) method and different sets of variables. The sets of variables investigated are as follows: (1) conservative variables; (2) pr...
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MDPI AG
2024-10-01
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| Series: | Fluids |
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| Online Access: | https://www.mdpi.com/2311-5521/9/11/248 |
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| author | Luca Alberti Emanuele Cammalleri Emanuele Carnevali Alessandra Nigro |
| author_facet | Luca Alberti Emanuele Cammalleri Emanuele Carnevali Alessandra Nigro |
| author_sort | Luca Alberti |
| collection | DOAJ |
| description | This article presents a comparison between the performance obtained by using a spatial discretization of the Euler equations based on a high-order discontinuous Galerkin (dG) method and different sets of variables. The sets of variables investigated are as follows: (1) conservative variables; (2) primitive variables based on pressure and temperature; (3) primitive variables based on the logarithms of pressure and temperature. The solution is advanced in time by using a linearly implicit high-order Rosenbrock-type scheme. The results obtained using the different sets are assessed across several canonical unsteady test cases, focusing on the accuracy, conservation properties and robustness of each discretization. In order to cover a wide range of physical flow conditions, the test-cases considered here are (1) the isentropic vortex convection, (2) the Kelvin–Helmholtz instability and (3) the Richtmyer–Meshkov instability. |
| format | Article |
| id | doaj-art-da546f327b664a3a87fc11149debacaf |
| institution | OA Journals |
| issn | 2311-5521 |
| language | English |
| publishDate | 2024-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fluids |
| spelling | doaj-art-da546f327b664a3a87fc11149debacaf2025-08-20T01:53:44ZengMDPI AGFluids2311-55212024-10-0191124810.3390/fluids9110248On the Use of Different Sets of Variables for Solving Unsteady Inviscid Flows with an Implicit Discontinuous Galerkin MethodLuca Alberti0Emanuele Cammalleri1Emanuele Carnevali2Alessandra Nigro3Department of Industrial Engineering and Mathematical Sciences (DIISM), Marche Polytechnic University, 60131 Ancona, ItalyDepartment of Industrial Engineering and Mathematical Sciences (DIISM), Marche Polytechnic University, 60131 Ancona, ItalyDepartment of Industrial Engineering and Mathematical Sciences (DIISM), Marche Polytechnic University, 60131 Ancona, ItalyDepartment of Industrial Engineering and Mathematical Sciences (DIISM), Marche Polytechnic University, 60131 Ancona, ItalyThis article presents a comparison between the performance obtained by using a spatial discretization of the Euler equations based on a high-order discontinuous Galerkin (dG) method and different sets of variables. The sets of variables investigated are as follows: (1) conservative variables; (2) primitive variables based on pressure and temperature; (3) primitive variables based on the logarithms of pressure and temperature. The solution is advanced in time by using a linearly implicit high-order Rosenbrock-type scheme. The results obtained using the different sets are assessed across several canonical unsteady test cases, focusing on the accuracy, conservation properties and robustness of each discretization. In order to cover a wide range of physical flow conditions, the test-cases considered here are (1) the isentropic vortex convection, (2) the Kelvin–Helmholtz instability and (3) the Richtmyer–Meshkov instability.https://www.mdpi.com/2311-5521/9/11/248discontinuous Galerkinconservative variablesprimitive variablesprimitive log variableslinearly implicit Rosenbrock schemesaccuracy properties |
| spellingShingle | Luca Alberti Emanuele Cammalleri Emanuele Carnevali Alessandra Nigro On the Use of Different Sets of Variables for Solving Unsteady Inviscid Flows with an Implicit Discontinuous Galerkin Method Fluids discontinuous Galerkin conservative variables primitive variables primitive log variables linearly implicit Rosenbrock schemes accuracy properties |
| title | On the Use of Different Sets of Variables for Solving Unsteady Inviscid Flows with an Implicit Discontinuous Galerkin Method |
| title_full | On the Use of Different Sets of Variables for Solving Unsteady Inviscid Flows with an Implicit Discontinuous Galerkin Method |
| title_fullStr | On the Use of Different Sets of Variables for Solving Unsteady Inviscid Flows with an Implicit Discontinuous Galerkin Method |
| title_full_unstemmed | On the Use of Different Sets of Variables for Solving Unsteady Inviscid Flows with an Implicit Discontinuous Galerkin Method |
| title_short | On the Use of Different Sets of Variables for Solving Unsteady Inviscid Flows with an Implicit Discontinuous Galerkin Method |
| title_sort | on the use of different sets of variables for solving unsteady inviscid flows with an implicit discontinuous galerkin method |
| topic | discontinuous Galerkin conservative variables primitive variables primitive log variables linearly implicit Rosenbrock schemes accuracy properties |
| url | https://www.mdpi.com/2311-5521/9/11/248 |
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