Numerical Method for Boltzmann Equation with Soroban-Grid CIP Method

Abstract

A new numerical scheme to solve the Boltzmann equation in phase space for rarefied gas is described on the basis of the Cubic Interpolated Propagation (CIP) method. The CIP procedure is extended to adaptive unstructured grid system by the Soroban grid. The grid points in velocity space can move dynamically following the spread of velocity space in a spatially localized manner. Such adaptively moving points in velocity space are similar to the particle codes but can provide higher-order-accurate solutions. Numerical solutions obtained by the Soroban-grid CIP are examined and the validity is discussed.