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Most of numerical methods for deterministic simulations of rarefied gas flowsuse the discrete velocity (or discrete ordinate) approximation. In thisapproach, the kinetic equation is approximated with a global velocity grid. Thegrid must be large and fine enough to capture all the distribution functions,which is very expensive for high speed flows (like in hypersonic aerodynamics).In this article, we propose to use instead different velocity grids that arelocal in time and space: these grids dynamically adapt to the width of thedistribution functions. The advantages and drawbacks of the method areillustrated in several 1D test cases.

Local discrete velocity grids for deterministic rarefied flow simulations