Unified computing methods for compressible and incompressible flows on staggered unstructured grids (DWI.5552)

A computing method is developed for fluid dynamics using unstructured grids, i.e. grids in which each vertex can belong to a different number of cells (in the interior of structured grids this number is fixed). Unstructured grids are of great importance for engineering applications, because a general consensus has arisen, that generation of structured grids for realistic applications cannot be automated to a sufficient extent, and putting in much human labor of a boring nature cannot be avoided. Unstructured grids do not suffer from this problem. For this reason, commercial CFD (computational fluid dynamics) code vendors and large research establishments are spending much effort to develop codes employing unstructured grids. This involves new algorithmic and theoretical developments in numerical analysis. We intend to support this trend in the present project, and to demonstrate the feasibility of an attractive new approach.

The project is innovative in two respects. In the first place, a staggered scheme (velocity and pressure located in different nodes) is used. This makes a second innovation possible: uniform applicability to compressible and incompressible flows. This desirable feature, not often found in other methods, is our main reason to adopt a specific staggered scheme. Furthermore, our recent work on the inviscid case leads us to believe that in the fully compressible case, where nonstaggered schemes are prevalent, staggered schemes are equally efficient and more versatile, allowing extension to general (e.g. nonconvex) equations of state and other features of flows with complicated physics (cavitation, multi-phase, magnetohydrodynamics).

A pilot code will be developed to demonstrate feasibility of the new method on industrial test examples. After completion of a doctoral thesis, a year will be devoted to extension of the functionality of the code and to elaboration of industrial applications.

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