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.

Unified solver for rarefied and continuum flows with adaptive mesh and algorithm refinement

“…This method has been used by Goldstein et al [29], Buet [30], Rogier and Schneider [31], Tan and Varghese [32] and Frolova and co-workers [2]. To illustrate the essence of the method, Fig.…”

“…The method is briefly described below. For arbitrary potential on intermolecular interactions, it is more convenient to perform integration over collision impact parameters (4) instead of integration over a unit sphere (2). The corresponding integral in the symmetric form with respect to direct and inverse collisions is…”

“…The development of hybrid solvers combining kinetic and fluid models has been an important area of research over the last decade (see Refs. [1,2] for reviews). Potential applications of such solvers range from high altitude flights to gas flows in micro systems.…”

Multi-scale Simulations of Gas Flows with Unified Flow Solver

“…[1] for review). Most researchers applied traditional DSMC methods for rarefied domains and identified statistical noise inherent to the particle methods as an obstacle for coupling kinetic and continuum solvers [2].…”

Coupling Atomistic and Continuum Models for Multi-scale Simulations of Gas Flows

“…The development of hybrid solvers combining kinetic and fluid models has been an important area of research over the last decade (see Refs. [1,2] for reviews). The challenges of developing multi-scale methods are physical and numerical.…”