A shock capturing method. (Russian. English summary) Zbl 1290.76056
Summary: Strong discontinuities, or shocks in continua are a result of external dynamic loads. On
the shock surface the conservation laws take the form of nonlinear algebraic equations for
jumps across the shock. Entropy jumps across a strong discontinuity, and just this jump
differs shocks from waves where the quantities vary continuously. In the heterogeneous
difference schemes, the shock is treated as a layer of a finite thickness comparable with
the cell size. This property of finite-difference schemes was called distraction. Since the
state behind a shock is related to the state before it by the Hugoniot, in the distraction
region there must act a mechanism that increases entropy. The physical viscosity and heat
conductivity in continuum mechanics equations do not make it unnecessary to introduce a
shock surface and hence cannot make the distraction length comparable with a few cells
of the difference mesh. The paper considers a number of finite difference schemes where
energy dissipation in the distraction region is defined by equations which are valid on the
shock surface.
MSC:
76L05 | Shock waves and blast waves in fluid mechanics |
74F10 | Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) |
76M25 | Other numerical methods (fluid mechanics) (MSC2010) |
74S30 | Other numerical methods in solid mechanics (MSC2010) |