Toward all speeds Euler/Navier-Stokes flow solutions on unstructured meshes

Abstract

Time i Unit vector tamgent to the control-volume surface u, V, w Velocity components in the x, y, and z coordinates, respectively U Velocity component in the direction of n (= K • n) V Volume V,-Median-dual control volume at a mesh point i 'Vceii Element control volimie Vn Overlapped control voltmie V Velocity vector Vn Velocity component normal to a surface Vt Velocity component tangent to a surface VNN Van Neumann nvimber X, y, z Cartesian coordinates Greek Symbols AQ At Time step Af.nt, Inviscid time step Atvis Viscous time step AXrm AYja Increments of x and y along the face m SW Characteristic variable set e Preconditioning scaling parameter Ci, £2 Empirically determined coefficients used in the dissipation terms of the central-difference-type discretization C3 Weighting parameter used in residucd-smoothing

Development of an explicit time accurate scheme for incompressible flows

“…The present work uses the spatial discretization of the conservation equations based on the SIMPLER [4] algorithm in the context of a multi-stage explicit time accurate Runge-Kutta algorithm for incompressible flows in primitive variables. The spatially discretized governing equations are rewritten and made suitable for integrating explicitly in time using the four-stage Runge-Kutta algorithm [9]. The basic principle of the new algorithm stems from the fact that pressure is the dominant driving force behind incompressible flows and that implicit treatment is required only for the pressure equation if at all necessary.…”