The mass-preserving and modified-upwind splitting DDM scheme for time-dependent convection–diffusion equations

Simulation of Multiphase Flows Using a Modified Upwind-Splitting Scheme

A robust AUSM upwind discretisation scheme has been developed to simulate multiphase flow using consistent spatial discretisation schemes and a modified low-Mach number diffusion term. The impact of the selection of an interfacial pressure model has also been investigated. Three representative test cases have been simulated to evaluate the accuracy of the commonly-used stiffenedgas equation of ...

Constraint-Preserving Upwind Methods for Multidimensional Advection Equations

A general framework for constructing constraint-preserving numerical methods is presented and applied to a multidimensional divergence-constrained advection equation. This equation is part of a set of hyperbolic equations that evolve a vector field while locally preserving either its divergence or curl. We discuss the properties of these equations and their relation to ordinary advection. Due t...

An Upwind-Differencing Scheme for the Incompressible Navier-Stokes Equations

Locally Divergence-preserving Upwind Finite Volume Schemes for Magnetohydrodynamic Equations

A main issue in nonstationary, compressible magnetohydrodynamic (MHD) simulations is controlling the divergence of the magnetic flux. This paper presents a general procedure showing how to modify the intercell fluxes in a conservative MHD finite volume code such that the scheme becomes locally divergence preserving. That is, a certain discrete divergence operator vanishes exactly during the ent...

A modified nodal scheme for the time-dependent, incompressible Navier–Stokes equations

Based on Poisson equation for pressure, a nodal numerical scheme is developed for the time-dependent, incompressible Navier–Stokes equations. Derivation is based on local transverse-integrations over finite size brick-like cells that transform each partial differential equation to a set of ordinary differential equations (ODEs). Solutions of these ODEs for the transverse-averaged dependent vari...