Abstract:
The splitting of a vector of Lax–Friedrichs and Rusanov type flows is considered, implemented in the form of splitting by physical processes: transfer processes. It is shown that it is a consequence of a single variable substitution. Two approaches to setting boundary conditions for problems with split flow vectors are proposed, ensuring zero splitting error. In accordance with these approaches, high-precision approximations of the boundary conditions of the first kind and the free exit for the quasi-linear transport equation, as well as the conditions of a rigid impermeable wall for the Eulerian equations, are constructed. A significant gain in accuracy from the use of new conditions in the application to bicompact schemes is demonstrated.
Key words:hyperbolic equations, compact schemes, bicompact schemes, splitting by physical processes, splitting of the flow vector, Lax–Friedrichs scheme, Rusanov scheme.
