Conservative upwind differencing for isentropic flows

The Upwind Differencing Method

The flux-vector and flux-difference splittings of Steger-Warming, Van Leer and Roe are tested in all possible combinations in the implicit and explicit operators that can be distinguished in implicit relaxation methods for the steady Euler and Navier-Stokes equations. The tests include one-dimensional inviscid nozzle flow, and two-dimensional inviscid and viscous shock reflection. Roe’s splitti...

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

High order conservative differencing for viscous terms and the application to vortex-induced vibration flows

A set of conservative 4th-order central differencing schemes for the viscous terms of Navier-Stokes equations are proved in this paper. These schemes are used with the 5th order WENO schemes for inviscid flux. The stencil width of the central differencing scheme is within that of the WENO scheme. The algorithm is used to simulate the vortex-induced oscillations of an elastically mounted circula...

Vortex-like finite-energy asymptotic profiles for isentropic compressible flows

Bidimensional incompressible viscous flows with well-localised vorticity are well-known to develop vortex structures. The purpose of the present paper is to recover the asymptotic profiles describing these phenomena for homogeneous finite-energy flows as asymptotic profiles for near-equilibrium isentropic compressible flows. This task is performed by extending the sharp description of the asymp...

A Divergence-Free Upwind Code for Multidimensional Magnetohydrodynamic Flows

A description is given for preserving ∇ · ~ B = 0 in a magnetohydrodynamic (MHD) code that employs the upwind, Total Variation Diminishing (TVD) scheme and the Strang-type operator splitting for multi-dimensionality. The method is based on the staggered mesh technique to constrain the transport of magnetic field: the magnetic field components are defined at grid interfaces with their advective ...