Abstract
Within a continuum framework, flows featuring shock waves can be modelled by means of either shock capturing or shock fitting. Shock-capturing codes are algorithmically simple, but are plagued by a number of numerical troubles, particularly evident when shocks are strong and the grids unstructured. On the other hand, shock-fitting algorithms on structured grids allow to accurately compute solutions on coarse meshes, but tend to be algorithmically complex. We show how recent advances in computational mesh generation allow to relieve some of the difficulties encountered by shock capturing and contribute towards making shock fitting on unstructured meshes a versatile technique.
Highlights
A shock wave is a surface in a flow-field across which various thermodynamic and kinematic properties of the fluid appear, from a macroscopic viewpoint, to change discontinuously
It is clear that Anisotropic Mesh Adaptation (AMA) allows to improve considerably the resolution of the interaction region; this allows to recognise the various flow features, which are indistinguishable in the solution computed on the uniform grid due to the large numerical thickness of the captured discontinuities in that region, and to reduce the disturbances that are generated along the bow shock: compare the density isolines computed within the shock layer
Building upon the authors’ experience in the field of the numerical simulation and of the development of numerical techniques, this paper highlights the strong relationship that exists between the development and application of mesh adaptation/refinement/generation techniques and the computation of high-quality solutions of flows featuring strong shocks
Summary
A shock wave is a surface in a flow-field across which various thermodynamic and kinematic properties of the fluid appear, from a macroscopic viewpoint, to change discontinuously. This new technique reduces significantly the algorithmic difficulties encountered in the previous implementations of the shock-fitting technique within the structured-grid context In this newly developed technique, the fitted shock fronts are moving boundaries that are free to float inside a computational domain discretized using triangles, in two space dimensions, or tetrahedra in three. The development of this new shock-fitting technique has been greatly furthered by the availability of public domain software libraries, developed over the last years, implementing a variety of tools for the generation of unstructured meshes This brief outline of the two types of numerical techniques used in the computation of flows featuring strong shocks highlights the role played by mesh generation/adaptation/refinement techniques in providing highquality solutions. Applications of the unstructured shock-fitting methodology both in two and three space dimensions is illustrated in Sections 3.1 and 3.2
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