A high order least square-based finite difference-finite volume method with lattice Boltzmann flux solver for simulation of incompressible flows on unstructured grids

YY Liu, C Shu, HW Zhang, LM Yang - Journal of Computational Physics, 2020 - Elsevier
This paper presents a high order least square-based finite difference-finite volume (LSFD-
FV) method together with lattice Boltzmann flux solver for accurate simulation of …

Third-order Paired Explicit Runge-Kutta schemes for stiff systems of equations

SH Nasab, BC Vermeire - Journal of Computational Physics, 2022 - Elsevier
The ability to advance locally-stiff systems of equations in time depends on accurate and
efficient temporal schemes. Recently, a new family of Paired Explicit Runge-Kutta (P-ERK) …

Spectral properties of high-order element types for implicit large eddy simulation

CA Pereira, BC Vermeire - Journal of Scientific Computing, 2020 - Springer
The use of high-order schemes continues to increase, with current methods becoming more
robust and reliable. The resolution of complex turbulent flows using Large Eddy Simulation …

Analysis of spectral volume methods for 1D linear scalar hyperbolic equations

W Cao, Q Zou - Journal of Scientific Computing, 2022 - Springer
This paper is concerned with the analysis of two spectral volume (SV) methods for 1D scalar
hyperbolic equations: one is constructed basing on the Gauss–Legendre points (LSV) and …

Spectral Volume from a DG perspective: Oscillation Elimination, Stability, and Optimal Error Estimates

Z Li, K Wu - arxiv preprint arxiv:2409.10871, 2024 - arxiv.org
The discontinuous Galerkin (DG) method and the spectral volume (SV) method are two
widely-used numerical methodologies for solving hyperbolic conservation laws. In this …

Analysis of a class of spectral volume methods for linear scalar hyperbolic conservation laws

J Lu, Y Jiang, CW Shu, M Zhang - Numerical Methods for …, 2024 - Wiley Online Library
In this article, we study the spectral volume (SV) methods for scalar hyperbolic conservation
laws with a class of subdivision points under the Petrov–Galerkin framework. Due to the …

High-order adaptive quadrature-free spectral volume method on unstructured grids

RE Harris, ZJ Wang - Computers & Fluids, 2009 - Elsevier
The high-order quadrature-free spectral volume (SV) method is extended to handle local
adaptive hp-refinement (grid and order refinement). Efficient edge-based adaptation utilizing …

Contributions to the development of residual discretizations for hyperbolic conservation laws with application to shallow water flows

M Ricchiuto - 2011 - theses.hal.science
In this work we review 12 years of developments in the field of residual based discretizations
and their application to the solution of the shallow water equations. Fundamental concepts …

Any order spectral volume methods for diffusion equations using the local discontinuous Galerkin formulation

J An, W Cao - ESAIM: Mathematical Modelling and Numerical …, 2023 - esaim-m2an.org
In this paper, we present and study two spectral volume (SV) schemes of arbitrary order for
diffusion equations by using the local discontinuous Galerkin formulation to discretize the …

[HTML][HTML] Eigenanalysis and non-modal analysis of collocated discontinuous Galerkin discretizations with the summation-by-parts property

IER Nolasco, A Er-Raiy, R Boukharfane… - … & Mathematics with …, 2022 - Elsevier
Guided by the von Neumann and non-modal analyses, we investigate the dispersion and
diffusion properties of collocated discontinuous Galerkin methods with the summation-by …