An Adaptive Hybrid (Cartesian-Prism) Grid and Flow Solver for Navier-Stokes Equations

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This Small Business Innovation Research Phase I project proposes to use overlapped Cartesian grid and Body-Fitted (BF) prism grids for solving viscous flow problems. Given a geometry definition in the form of triangularized surfaces, a BF prism mesh will be generated using the advancing layers technology with grid clustering near body surfaces. This prism mesh is then overlapped with a coarse uniform Cartesian background grid. Initially the Cartesian grid will be refined to have similar resolution near the prism grid. A high-order flow solver based on linear reconstruction and Roe's flux-difference splitting will be developed. Grid adaptation according to the physical nature of the flow field will be carried out to place control volumes where required the most, achieving maximum accuracy with minimum resources. An explicit multi-grid procedure will be employed to speed up the simulation process. The interface between the Cartesian and prism grid will be treated by conserving mass, momentum and energy flux on the outer boundary of the prism grid. The overall algorithm integrates grid generation and flow solver into one complete system to obtain maximum solution accuracy, efficiency and user friendliness. In Phase I, the above methodology will be implemented and demonstrated for 2-D viscous flow problems. Extension to 3-D and moving body problems and implementation in a commercial code will be made in Phase II.