A parallel p ‐adaptive discontinuous Galerkin method for the Euler equations with dynamic load‐balancing on tetrahedral grids

A novel p ‐adaptive discontinuous Galerkin (DG) method has been developed to solve the Euler equations on three‐dimensional tetrahedral grids. Hierarchical orthogonal basis functions are adopted for the DG spatial discretization while a third order TVD Runge‐Kutta method is used for the time integra...

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Veröffentlicht in:International journal for numerical methods in fluids 2023-12, Vol.95 (12), p.1913-1932
Hauptverfasser: Li, Weizhao, Pandare, Aditya K., Luo, Hong, Bakosi, Jozsef, Waltz, Jacob
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container_end_page 1932
container_issue 12
container_start_page 1913
container_title International journal for numerical methods in fluids
container_volume 95
creator Li, Weizhao
Pandare, Aditya K.
Luo, Hong
Bakosi, Jozsef
Waltz, Jacob
description A novel p ‐adaptive discontinuous Galerkin (DG) method has been developed to solve the Euler equations on three‐dimensional tetrahedral grids. Hierarchical orthogonal basis functions are adopted for the DG spatial discretization while a third order TVD Runge‐Kutta method is used for the time integration. A vertex‐based limiter is applied to the numerical solution in order to eliminate oscillations in the high order method. An error indicator constructed from the solution of order and is used to adapt degrees of freedom in each computational element, which remarkably reduces the computational cost while still maintaining an accurate solution. The developed method is implemented with under the Charm++ parallel computing framework. Charm++ is a parallel computing framework that includes various load‐balancing strategies. Implementing the numerical solver under Charm++ system provides us with access to a suite of dynamic load balancing strategies. This can be efficiently used to alleviate the load imbalances created by p ‐adaptation. A number of numerical experiments are performed to demonstrate both the numerical accuracy and parallel performance of the developed p ‐adaptive DG method. It is observed that the unbalanced load distribution caused by the parallel p ‐adaptive DG method can be alleviated by the dynamic load balancing from Charm++ system. Due to this, high performance gain can be achieved. For the testcases studied in the current work, the parallel performance gain ranged from 1.5× to 3.7×. Therefore, the developed p ‐adaptive DG method can significantly reduce the total simulation time in comparison to the standard DG method without p ‐adaptation.
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Hierarchical orthogonal basis functions are adopted for the DG spatial discretization while a third order TVD Runge‐Kutta method is used for the time integration. A vertex‐based limiter is applied to the numerical solution in order to eliminate oscillations in the high order method. An error indicator constructed from the solution of order and is used to adapt degrees of freedom in each computational element, which remarkably reduces the computational cost while still maintaining an accurate solution. The developed method is implemented with under the Charm++ parallel computing framework. Charm++ is a parallel computing framework that includes various load‐balancing strategies. Implementing the numerical solver under Charm++ system provides us with access to a suite of dynamic load balancing strategies. This can be efficiently used to alleviate the load imbalances created by p ‐adaptation. A number of numerical experiments are performed to demonstrate both the numerical accuracy and parallel performance of the developed p ‐adaptive DG method. It is observed that the unbalanced load distribution caused by the parallel p ‐adaptive DG method can be alleviated by the dynamic load balancing from Charm++ system. Due to this, high performance gain can be achieved. For the testcases studied in the current work, the parallel performance gain ranged from 1.5× to 3.7×. Therefore, the developed p ‐adaptive DG method can significantly reduce the total simulation time in comparison to the standard DG method without p ‐adaptation.</description><identifier>ISSN: 0271-2091</identifier><identifier>EISSN: 1097-0363</identifier><identifier>DOI: 10.1002/fld.5231</identifier><language>eng</language><publisher>Bognor Regis: Wiley Subscription Services, Inc</publisher><subject>Adaptation ; adaptivity ; Basis functions ; compressible flow ; Computer applications ; Computing costs ; discontinuous Galerkin ; Dynamic loads ; Euler flow ; Euler-Lagrange equation ; Eulers equations ; Galerkin method ; Load balancing ; Load distribution ; Load distribution (forces) ; Mathematical analysis ; mesh adaptation ; Orthogonal functions ; Oscillations ; parallelization ; Time integration</subject><ispartof>International journal for numerical methods in fluids, 2023-12, Vol.95 (12), p.1913-1932</ispartof><rights>2023. 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Hierarchical orthogonal basis functions are adopted for the DG spatial discretization while a third order TVD Runge‐Kutta method is used for the time integration. A vertex‐based limiter is applied to the numerical solution in order to eliminate oscillations in the high order method. An error indicator constructed from the solution of order and is used to adapt degrees of freedom in each computational element, which remarkably reduces the computational cost while still maintaining an accurate solution. The developed method is implemented with under the Charm++ parallel computing framework. Charm++ is a parallel computing framework that includes various load‐balancing strategies. Implementing the numerical solver under Charm++ system provides us with access to a suite of dynamic load balancing strategies. This can be efficiently used to alleviate the load imbalances created by p ‐adaptation. A number of numerical experiments are performed to demonstrate both the numerical accuracy and parallel performance of the developed p ‐adaptive DG method. It is observed that the unbalanced load distribution caused by the parallel p ‐adaptive DG method can be alleviated by the dynamic load balancing from Charm++ system. Due to this, high performance gain can be achieved. For the testcases studied in the current work, the parallel performance gain ranged from 1.5× to 3.7×. 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1097-0363
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subjects Adaptation
adaptivity
Basis functions
compressible flow
Computer applications
Computing costs
discontinuous Galerkin
Dynamic loads
Euler flow
Euler-Lagrange equation
Eulers equations
Galerkin method
Load balancing
Load distribution
Load distribution (forces)
Mathematical analysis
mesh adaptation
Orthogonal functions
Oscillations
parallelization
Time integration
title A parallel p ‐adaptive discontinuous Galerkin method for the Euler equations with dynamic load‐balancing on tetrahedral grids
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