Compound difference schemes for time-dependent equations on non-uniform nets

Abstract

A new approach to constructing monotonous second-order-accurate schemes for time-dependent Navier-Stokes equations in the compressible case is suggested. Flows with shock waves and thin viscous boundary layers are considered. The approach joins two different schemes while each of them is appropriate for its own type of flow. The resulting scheme is constructed as a splitting one, and the approach is applied at the stage governed by the Euler equations in Lagrangian variables. The approach turns out to be fruitful also for parabolic equations with ‘viscous’ terms. The method is illustrated by the problem on compression of deuterium in a conical solid-body target with viscous heating of deuterium.