UNIFORMLY ACCURATE SCHEMES FOR HYPERBOLIC SYSTEMS WITH RELAXATION

We develop high-resolution shock-capturing numerical schemes for hyper bolic systems with relaxation. In such systems the relaxation time may vary from order-1 to much less than unity. When the relaxation time i s small, the relaxation term becomes very strong and highly stiff, and underresolved numerical schemes mag. produce spurious results. Usuall y one cannot decouple the problem into separate regimes and handle dif ferent regimes with different methods. Thus it is important to have a scheme that works uniformly with respect to the relaxation time. Using the Broadwell model of the nonlinear Boltzmann equation we develop a second-order scheme that works effectively, with a fixed spatial and t emporal discretization, for all ranges of the mean free path. Formal u niform consistency proof for a first-order scheme and numerical conver gence proof for the second-order scheme are also presented. We also ma ke numerical comparisons of the new scheme with some other schemes. Th is study is motivated by the reentry problem in hyper sonic computatio ns.