Related papers: New Adaptive Low-Dissipation Central-Upwind Scheme…
The scale-resolving simulation of high speed compressible flow through direct numerical simulation (DNS) or large eddy simulation (LES) requires shock-capturing schemes to be more accurate for resolving broadband turbulence and robust for…
This article performs a unified convergence analysis of a variety of numerical methods for a model of the miscible displacement of one incompressible fluid by another through a porous medium. The unified analysis is enabled through the…
This work introduces an optimization-based $rp$-adaptive numerical method to approximate solutions of viscous, shock-dominated flows using implicit shock tracking and a high-order discontinuous Galerkin discretization on traditionally…
OpenFOAM is a widely used computational fluid dynamics (CFD) framework based on the finite volume method for solving a wide range of flow problems. However, its default numerical schemes, particularly the Kurganov-Noelle-Petrova (KNP)…
This paper develops entropy stable (ES) adaptive moving mesh schemes for the 2D and 3D special relativistic hydrodynamic (RHD) equations. They are built on the ES finite volume approximation of the RHD equations in curvilinear coordinates,…
This paper introduces a novel approach to compute the numerical fluxes at the cell boundaries for a cell-centered conservative numerical scheme. Explicit gradients used in deriving the reconstruction polynomials are replaced by high-order…
In this work, we develop a robust adaptive well-balanced and positivity-preserving central-upwind scheme on unstructured triangular grids for shallow water equations. The numerical method is an extension of the scheme from [{\sc Liu {\em et…
We assess the validity of a single step Godunov scheme for the solution of the magneto-hydrodynamics equations in more than one dimension. The scheme is second-order accurate and the temporal discretization is based on the dimensionally…
Explicit non-oscillatory central difference schemes become excessively diffusive when applied to highly nonlinear advection problems where small time steps are necessary to maintain stability. Here, we present a correction to reduce such…
We introduce stabilized spline collocation schemes for the numerical solution of nonlinear, hyperbolic conservation laws. A nonlinear, residual-based viscosity stabilization is combined with a projection stabilization-inspired linear…
Simulations of single- and multi-species compressible flows with shock waves and discontinuities are conducted using a weighted compact nonlinear scheme (WCNS) with a newly developed sixth order localized dissipative interpolation. In…
We study a method based on Balancing Domain Decomposition by Constraints (BDDC) for a numerical solution of a single-phase flow in heterogenous porous media. The method solves for both flux and pressure variables. The fluxes are resolved in…
We propose a time-adaptive predictor/multi-corrector method to solve hyperbolic partial differential equations, based on the generalized-$\alpha$ scheme that provides user-control on the numerical dissipation and second-order accuracy in…
In this paper, we propose a new set of midpoint-based high-order discretization schemes for computing straight and mixed nonlinear second derivative terms that appear in the compressible Navier-Stokes equations. Firstly, we detail a set of…
This paper introduces a novel adaptive framework for processing dynamic flow signals over simplicial complexes, extending classical least-mean-squares (LMS) methods to high-order topological domains. Building on discrete Hodge theory, we…
We present a linear, second order fully discrete numerical scheme on a staggered grid for a thermodynamically consistent hydrodynamic phase field model of binary compressible fluid flow mixtures derived from the generalized Onsager…
The equations of Lagrangian gas dynamics fall into the larger class of overdetermined hyperbolic and thermodynamically compatible (HTC) systems of partial differential equations. They satisfy an entropy inequality (second principle of…
We describe an implementation of compressible inviscid fluid solvers with block-structured adaptive mesh refinement on Graphics Processing Units using NVIDIA's CUDA. We show that a class of high resolution shock capturing schemes can be…
A second-order-accurate finite volume method, hybridized by blending an extended double-flux algorithm and a traditionally conservative scheme, is developed. In this scheme, hybrid convective fluxes as well as hybrid interpolation…
Solving compressible flows containing discontinuities remains a major challenge for numerical methods especially on unstructured grids. Thus in this work, we make contributions to shock capturing schemes on unstructured grids with aim of…