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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Main Authors: Luca Alberti, Emanuele Cammalleri, Emanuele Carnevali, Alessandra Nigro
Format: Article
Language:English
Published: MDPI AG 2024-10-01
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.
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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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AT emanuelecarnevali ontheuseofdifferentsetsofvariablesforsolvingunsteadyinviscidflowswithanimplicitdiscontinuousgalerkinmethod
AT alessandranigro ontheuseofdifferentsetsofvariablesforsolvingunsteadyinviscidflowswithanimplicitdiscontinuousgalerkinmethod