SHOCK WAVE CAPTURING WITH MULTI-GRID ACCELERATED, SOLUTION ADAPTIVE, CARTESIAN GRID BASED NAVIER STOKES SOLVER

Abstract

Cartesian grids employ specially designed algorithms to generate automatic grids for complex geometries and to simulate flows around such geometries regardless of the body shape and number of bodies. The main advantage of Cartesian methods over the body-conformal approach is that without regard to drawbacks of the geometric complexity of the embedded boundaries, the computational grid does not alter except close to all boundaries where cutcells are employed. In this study, implementation of generated two-dimensional adaptive refinement/coarsening scheme codes is appended to the developed compressible flow solver by using special Cartesian-based algorithms. Cartesian grids are generated by constructing a quadtree based data structure in two-dimensional flows. By means of solution adaptation, a finer grid is obtained around a shock wave. Convergence rate is increased with multi-grid method. Thus, a “hands-off”, Cartesian grid generator based flow solver is implemented in object-oriented FORTRAN programming language. The solutions are validated by comparing the results with experimental and numerical data available in literature for the supersonic flow around NACA 0012 airfoil. Employing the solution adaptation techniques, Mach contours of the flow around the wing have verified and captured the shock wave by the developed GeULER-NS (cartesian-Grid-generator-with-eULER-and-Navier-Stokes-flow-solver) code.

Keywords

• Cartesian Grid Generation
• Object-oriented Programming
• Solution Adaptation
• Multi-grid Method