Viscous and elastic stress tensors in hydrodynamic computations

Abstract The properties of the stress tensor in hydrodynamics and the dynamic theory of elasticity are considered. The properties are analysed by including the tensor mathematical viscosity in the numerical algorithm for calculating hydrodynamic flows. This viscosity preserves the property of the scalar viscosity usually used to perform through-calculation of flows with shock waves and prevents the results from being non-monotonic. The unified approach to the approximation of the viscous and elastic stress tensors enables a calculation to be made of problems of the interaction of fluid or gas flow with elastic obstacles. The method is illustrated by the example of the detonation of a substance inside an elastic shell and the deformation of the latter under the action of the detonation and shock waves.