Modeling Error in L1 for a Hierarchy of 1-D Discrete Velocity Models

Abstract

We consider the spatial difference in L 1 between solutions to two different discrete velocity models in one space dimension. We assume that the second (fine) model is obtained by adding new velocities to the first (coarse) model, although the collision operators can be completely different. The 1-D discrete velocity models studied here include projections of n-D models, as described by Beale. This work adapts the nonlinear and decreasing interaction functional of Ha and Tzavaras for discrete velocity models in 1-D in order to measure the distance in L 1 . The resulting functional increases by a term proportional to the residual of the modeling error for the coarse model. The modeling error can therefore be computed a posteriori and can be used to determine which discrete velocity model within a hierarchy satisfies a prescribed accuracy.