Gridless Compressible Flow: A White Paper

In this paper the development of a gridless method to solve compressible flow problems is discussed. The governing evolution equations for velocity divergence {delta}, vorticity {omega}, density {rho}, and temperature T are obtained from the primitive variable Navier-Stokes equations. Simplifications to the equations resulting from assumptions of ideal gas behavior, adiabatic flow, and/or constant viscosity coefficients are given. A general solution technique is outlined with some discussion regarding alternative approaches. Two radial flow model problems are considered which are solved using both a finite difference method and a compressible particle method. The first of these is an isentropic inviscid 1D spherical flow which initially has a Gaussian temperature distribution with zero velocity everywhere. The second problem is an isentropic inviscid 2D radial flow which has an initial vorticity distribution with constant temperature everywhere. Results from the finite difference and compressible particle calculations are compared in each case. A summary of the results obtained herein is given along with recommendations for continuing the work.