Calculating three-dimensional fluid flows at all speeds with an Eulerian-Lagrangian computing mesh

Abstract

A computing technique is presented for the calculation of three-dimensional, time-dependent fluid dynamics problems. The full nonlinear Navier-Stokes equations are solved with a finite-difference scheme based upon an Arbitrary Lagrangian-Eulerian (ALE) computing mesh with vertices that may move with the fluid (Lagrangian), remain fixed (Eulerian), or move in any prescribed manner. The method is applicable to three-dimensional flows at all speeds, employing an implicit formulation similar to the Implicit Continuous-Fluid Eulerian (ICE) technique. Marker particles are used that may follow exactly the motion of the fluid to aid in flow visualization, or they can represent particulate matter whose behavior is affected by inertia, drag, gravity, and molecular and turbulent diffusion. Calculational examples are shown in the form of a variety of perspective view plots.