High‐order CFD methods: current status and perspective
After several years of planning, the 1st International Workshop on High‐Order CFD Methods
was successfully held in Nashville, Tennessee, on January 7–8, 2012, just before the 50th …
was successfully held in Nashville, Tennessee, on January 7–8, 2012, just before the 50th …
Compact high order finite volume method on unstructured grids III: Variational reconstruction
This paper presents a variational reconstruction for the high order finite volume method in
solving the two-dimensional Navier–Stokes equations on arbitrary unstructured grids. In the …
solving the two-dimensional Navier–Stokes equations on arbitrary unstructured grids. In the …
A general framework to construct schemes satisfying additional conservation relations. Application to entropy conservative and entropy dissipative schemes
R Abgrall - Journal of Computational Physics, 2018 - Elsevier
We are interested in the approximation of a steady hyperbolic problem. In some cases, the
solution can satisfy an additional conservation relation, at least when it is smooth. This is the …
solution can satisfy an additional conservation relation, at least when it is smooth. This is the …
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 …
Reinterpretation and extension of entropy correction terms for residual distribution and discontinuous Galerkin schemes: application to structure preserving …
For the general class of residual distribution (RD) schemes, including many finite element
(such as continuous/discontinuous Galerkin) and flux reconstruction methods, an approach …
(such as continuous/discontinuous Galerkin) and flux reconstruction methods, an approach …
WENO schemes on arbitrary unstructured meshes for laminar, transitional and turbulent flows
This paper presents the development and implementation of weighted-essentially-non-
oscillatory (WENO) schemes for viscous flows on arbitrary unstructured grids. WENO …
oscillatory (WENO) schemes for viscous flows on arbitrary unstructured grids. WENO …
Multi-dimensional limiting process for finite volume methods on unstructured grids
This paper deals with a robust, accurate and efficient multi-dimensional limiting strategy on
three-dimensional unstructured grids within the framework of finite volume method. The …
three-dimensional unstructured grids within the framework of finite volume method. The …
High-order solution-adaptive central essentially non-oscillatory (CENO) method for viscous flows
A high-order, central, essentially non-oscillatory (CENO), finite-volume scheme in
combination with a block-based adaptive mesh refinement (AMR) algorithm is proposed for …
combination with a block-based adaptive mesh refinement (AMR) algorithm is proposed for …
High order schemes for hyperbolic problems using globally continuous approximation and avoiding mass matrices
R Abgrall - Journal of Scientific Computing, 2017 - Springer
When integrating unsteady problems using globally continuous representation of the
solution, as for continuous finite element methods, one faces the problem of inverting a mass …
solution, as for continuous finite element methods, one faces the problem of inverting a mass …
Uncertainty quantification for hyperbolic systems of conservation laws
We review uncertainty quantification (UQ) for hyperbolic systems of conservation (balance)
laws. The input uncertainty could be in the initial data, fluxes, coefficients, source terms or …
laws. The input uncertainty could be in the initial data, fluxes, coefficients, source terms or …