High order entropy preserving ADER-DG schemes
In this paper, we develop a fully discrete entropy preserving ADER-Discontinuous Galerkin
(ADER-DG) method. To obtain this desired result, we equip the space part of the method …
(ADER-DG) method. To obtain this desired result, we equip the space part of the method …
Hyperbolic balance laws: residual distribution, local and global fluxes
R Abgrall, M Ricchiuto - Numerical Fluid Dynamics: Methods and …, 2022 - Springer
This review paper describes a class of scheme named “residual distribution schemes” or
“fluctuation splitting schemes”. They are a generalization of Roe's numerical flux in …
“fluctuation splitting schemes”. They are a generalization of Roe's numerical flux in …
High-order accurate entropy-stable discontinuous collocated Galerkin methods with the summation-by-parts property for compressible CFD frameworks: Scalable …
This work reports on the performances of a fully-discrete hp-adaptive entropy stable
discontinuous collocated Galerkin method for the compressible Naiver–Stokes equations …
discontinuous collocated Galerkin method for the compressible Naiver–Stokes equations …
On the robustness and performance of entropy stable collocated discontinuous Galerkin methods
In computational fluid dynamics, the demand for increasingly multidisciplinary reliable
simulations, for both analysis and design optimization purposes, requires transformational …
simulations, for both analysis and design optimization purposes, requires transformational …
Fully well-balanced entropy controlled discontinuous Galerkin spectral element method for shallow water flows: global flux quadrature and cell entropy correction
We present a novel formulation of the discontinuous Galerkin spectral element method for
solving balance laws, with application to the shallow water equations. The scheme …
solving balance laws, with application to the shallow water equations. The scheme …
On improving the efficiency of ADER methods
The (modern) arbitrary derivative (ADER) approach is a popular technique for the numerical
solution of differential problems based on iteratively solving an implicit discretization of their …
solution of differential problems based on iteratively solving an implicit discretization of their …
Well balanced residual distribution for the ALE spherical shallow water equations on moving adaptive meshes
L Arpaia, M Ricchiuto - Journal of Computational Physics, 2020 - Elsevier
We consider the numerical approximation of the Shallow Water Equations (SWEs) in
spherical geometry for oceanographic applications. To provide enhanced resolution of …
spherical geometry for oceanographic applications. To provide enhanced resolution of …
Extrapolated DIscontinuity Tracking for complex 2D shock interactions
A new shock-tracking technique that avoids re-meshing the computational grid around the
moving shock-front was recently proposed by the authors (Ciallella et al., 2020). The method …
moving shock-front was recently proposed by the authors (Ciallella et al., 2020). The method …
High-order gradients with the shifted boundary method: an embedded enriched mixed formulation for elliptic PDEs
We propose an extension of the embedded boundary method known as “shifted boundary
method” to elliptic diffusion equations in mixed form (eg, Darcy flow, heat diffusion problems …
method” to elliptic diffusion equations in mixed form (eg, Darcy flow, heat diffusion problems …
r-adaptive algorithms for supersonic flows with high-order Flux Reconstruction methods
The present paper addresses the development and implementation of the first r-adaptive
mesh refinement (r-AMR) algorithm for a high-order Flux Reconstruction solver. The r …
mesh refinement (r-AMR) algorithm for a high-order Flux Reconstruction solver. The r …