Very high order treatment of embedded curved boundaries in compressible flows: ADER discontinuous Galerkin with a space-time Reconstruction for Off-site data
GABURRO, Elena
Certified Adaptive discRete moDels for robust simulAtions of CoMplex flOws with Moving fronts [CARDAMOM]
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Certified Adaptive discRete moDels for robust simulAtions of CoMplex flOws with Moving fronts [CARDAMOM]
GABURRO, Elena
Certified Adaptive discRete moDels for robust simulAtions of CoMplex flOws with Moving fronts [CARDAMOM]
Certified Adaptive discRete moDels for robust simulAtions of CoMplex flOws with Moving fronts [CARDAMOM]
RICCHIUTO, Mario
Certified Adaptive discRete moDels for robust simulAtions of CoMplex flOws with Moving fronts [CARDAMOM]
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Certified Adaptive discRete moDels for robust simulAtions of CoMplex flOws with Moving fronts [CARDAMOM]
Idioma
en
Document de travail - Pré-publication
Este ítem está publicado en
2023
Resumen en inglés
In this paper we present a novel approach for the design of high order general boundary conditions when approximating solutions of the Euler equations on domains with curved boundaries, using meshes which may not be boundary ...Leer más >
In this paper we present a novel approach for the design of high order general boundary conditions when approximating solutions of the Euler equations on domains with curved boundaries, using meshes which may not be boundary conformal. When dealing with curved boundaries and/or unfitted discretizations, the consistency of boundary conditions is a well-known challenge, especially in the context of high order schemes. In order to tackle such consistency problems, the so-called Reconstruction for Off-site Data (ROD) method has been recently introduced in the finite volume framework: it is based on performing a boundary polynomial reconstruction that embeds the considered boundary treatment thanks to the implementation of a constrained minimization problem. This work is devoted to the development of the ROD approach in the context of discontinuous finite elements. We use the genuine space-time nature of the local ADER predictors to reformulate the ROD as a single space-time reconstruction procedure. This allows us to avoid a new reconstruction (linear system inversion) at each sub-time node and retrieve a single space-time polynomial that embeds the considered boundary conditions for the entire space-time element. Several numerical experiments are presented proving the consistency of the new approach for all kinds of boundary conditions. Computations involving the interaction of shocks with embedded curved boundaries are made possible through an a posteriori limiting technique.< Leer menos
Palabras clave en inglés
Curved boundaries
Space-time schemes
Unfitted discretization
Discontinuous Galerkin
compressible flows
Numerical Analysis (math.NA)
FOS: Mathematics
Orígen
Importado de HalCentros de investigación