In this paper, we introduce and test the enhanced stability recovery (ESR) scheme. It is a robust and compact approach to the computation of diffusive fluxes in the framework of discontinuous Galerkin methods. The scheme is characterized by a new recovery basis and a new procedure for the weak imposition of Dirichlet boundary conditions. These features make the method flexible and robust, even in the presence of highly distorted meshes. The implementation is simplified with respect to the original recovery scheme (RDG1x). Furthermore, thanks to the proposed approach, a robust implementation of p-adaptive algorithms is possible. Numerical tests on unstructured grids show a convergence rate equal to p + 1, where p is the reconstruction order. Comparisons are shown with the original recovery scheme RDG1x and the widely used BR2 method. Results show a significantly larger stability region for the proposed discretization when explicit Runge-Kutta time integration is employed. Interestingly, this advantage grows quickly when the reconstruction order is increased. The proposed procedure for the weak imposition of Dirichlet boundary conditions does not need the introduction of ghost cells, and it is truly local because it does not require data exchange with other elements. It can be easily used with curvilinear wall elements. Several test cases are considered. They include some benchmark tests with the heat equation and compressible Navier-Stokes equations, with test cases designed also to evaluate the behaviour of the scheme with very stretched elements and separated flows. Copyright (c) 2014 John Wiley & Sons, Ltd.

A robust and adaptive recovery-based discontinuous Galerkin method for the numerical solution of convection-diffusion equations

PUPPO, GABRIELLA ANNA
2015

Abstract

In this paper, we introduce and test the enhanced stability recovery (ESR) scheme. It is a robust and compact approach to the computation of diffusive fluxes in the framework of discontinuous Galerkin methods. The scheme is characterized by a new recovery basis and a new procedure for the weak imposition of Dirichlet boundary conditions. These features make the method flexible and robust, even in the presence of highly distorted meshes. The implementation is simplified with respect to the original recovery scheme (RDG1x). Furthermore, thanks to the proposed approach, a robust implementation of p-adaptive algorithms is possible. Numerical tests on unstructured grids show a convergence rate equal to p + 1, where p is the reconstruction order. Comparisons are shown with the original recovery scheme RDG1x and the widely used BR2 method. Results show a significantly larger stability region for the proposed discretization when explicit Runge-Kutta time integration is employed. Interestingly, this advantage grows quickly when the reconstruction order is increased. The proposed procedure for the weak imposition of Dirichlet boundary conditions does not need the introduction of ghost cells, and it is truly local because it does not require data exchange with other elements. It can be easily used with curvilinear wall elements. Several test cases are considered. They include some benchmark tests with the heat equation and compressible Navier-Stokes equations, with test cases designed also to evaluate the behaviour of the scheme with very stretched elements and separated flows. Copyright (c) 2014 John Wiley & Sons, Ltd.
Boundary conditions; Discontinuous Galerkin; Navier-Stokes; p-adaptivity; Recovery method; Stability;
Ferrero, A.; Larocca, F.; Puppo, GABRIELLA ANNA
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11383/2024826
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 24
  • ???jsp.display-item.citation.isi??? 18
social impact