Construction of a Unified Continuum/Kinetic Solver for Aerodynamic Problems

Abstract

We describe our progress toward the development of a unified flow solver (UFS) that can automatically separate nonequilibrium and near-equilibrium domains and switch between continuum and kinetic solvers to combine the efficiency of continuum models with the accuracy of kinetic models. Direct numerical solution of the Boltzmann transport equation is used in kinetic regions, whereas kinetic schemes of gas dynamics are used elsewhere. The efficiency and numerical stability of the UFS is attained by using similar computational techniques for the kinetic and continuum solvers and by employing intelligent domain decomposition algorithms. Different criteria for identifying kinetic and continuum areas and two different mechanisms of coupling Boltzmann and Euler solvers are explored. Solutions of test problems with small Knudsen number are presented to illustrate the capabilities of the UFS for different conditions. It is shown that the UFS can automatically introduce and remove kinetic patches to maximize the accuracy and efficiency of simulations. To our knowledge, this is the first attempt to use direct Boltzmann and continuum flow solvers for developing a hybrid code with solution adaptive domain decomposition.