Related papers: Strang splitting structure-preserving high-order c…
In general, high order splitting methods suffer from an order reduction phenomena when applied to the time integration of partial differential equations with non-periodic boundary conditions. In the last decade, there were introduced…
Splitting methods are a widely used numerical scheme for solving convection-diffusion problems. However, they may lose stability in some situations, particularly when applied to convection-diffusion problems in the presence of an unbounded…
An initial-boundary value problem for the $n$-dimensional ($n\geq 2$) time-dependent Schr\"odinger equation in a semi-infinite (or infinite) parallelepiped is considered. Starting from the Numerov-Crank-Nicolson finite-difference scheme, we…
In this paper we study the problem of computing the effective diffusivity for a particle moving in chaotic and stochastic flows. In addition we numerically investigate the residual diffusion phenomenon in chaotic advection. The residual…
The two-dimensional unsteady coupled Burgers' equations with moderate to severe gradients, are solved numerically using higher-order accurate finite difference schemes; namely the fourth-order accurate compact ADI scheme, and the…
In this study, we propose a genuine fourth-order compact finite difference scheme for solving biharmonic equations with Dirichlet boundary conditions in both two and three dimensions. In the 2D case, we build upon the high-order compact…
In this study, we investigate the Shallow Water Equations incorporating source terms accounting for Manning friction and a non-flat bottom topology. Our primary focus is on developing and validating numerical schemes that serve a dual…
We propose a Hybrid High-Order (HHO) formulation of the incompressible Navier-Stokes equations with variable density that provides exact conservation of volume and, accordingly, pure advection of the density variable. The spatial…
In this article, we have developed a higher order compact numerical method for variable coefficient parabolic problems with mixed derivatives. The finite difference scheme, presented here for two-dimensional domains, is based on fourth…
We propose a high-order finite element method for linear fourth-order elliptic problems that is both nodally bound-preserving and mass-conservative, based on a variational inequality formulation. The method admits an equivalent strictly…
The goal of the present work is to solve a linear dispersive equation with variable coefficient advection on an unbounded domain. In this setting, transparent boundary conditions are vital to allow waves to leave (or even re-enter) the,…
This work introduces a new higher-order super-compact (HOSC) implicit finite difference scheme for analyzing three-dimensional (3D) natural convection and entropy generation in non-Newtonian fluids. The proposed scheme achieves fourth-order…
In this work, we show high order splitting methods of integration without negative steps, allowing us to solve numerically irreversible problems, like reaction-diffusion equations. The methods consist in a suitable affine combinations of…
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…
A high-order finite element method is proposed to solve the nonlinear convection-diffusion equation on a time-varying domain whose boundary is implicitly driven by the solution of the equation. The method is semi-implicit in the sense that…
Different relaxation approximations to partial differential equations, including conservation laws, Hamilton-Jacobi equations, convection-diffusion problems, gas dynamics problems, have been recently proposed. The present paper focuses onto…
We are interested in the high-order approximation of anisotropic, potential-driven advection-diffusion models on general polytopal partitions. We study two hybrid schemes, both built upon the Hybrid High-Order technology. The first one…
Shallow water surface flows commonly entrain sediments, resulting in scouring and/or deposition of the underlying substrate that may strongly influence the pattern of subsequent flow. These coupled phenomena, which can be investigated…
This work proposes an efficient space-time two-grid compact difference (ST-TGCD) scheme for solving the two-dimensional (2D) viscous Burgers' equation subject to initial and periodic boundary conditions. The proposed approach combines a…
We solve the convection-diffusion equation using a coupling of cell-centered finite volume (FV) and discontinuous Galerkin (DG) methods. The domain is divided into disjoint regions assigned to FV or DG, and the two methods are coupled…