The method of space-time conservation element and solution element - Applications to one-dimensional and two-dimensional time-marching flow problems

Sin-Chung Chang, Xiao-Yen Wang, Chuen-Yen Chow
1995 12th Computational Fluid Dynamics Conference   unpublished
A nontraditional numerical method for solving conservation laws is being developed. The new method is designed from a physicist's perspective, i.e., its development is based more on physics than numerics. Even though it uses only the simplest approximation techniques, a 2D time-marching Euler solver developed recently using the new method is capable of generating nearly perfect solutions for a 2D shock reflection problem used by Helen Yee and others. Moreover, a recent application of this
more » ... to computational aeroacoustics (CAA) problems reveals that: (i) accuracy of its results is comparable to that of a 6th order compact difference scheme even though nominally the current solver is only of 2nd-order accuracy; (ii) generally, the non-reflecting boundary condition can be implemented in a simple way without involving characteristic variables; and (iii) most importantly, the current solver is capable of handling both continuous and discontinuous flows very well and thus provides a unique numerical tool for solving those flow problems where the interactions between sound waves and shocks are important, such as the noise field around a supersonic over-or under-expansion jet.
doi:10.2514/6.1995-1754 fatcat:mmpzpxcbxjffjcrxdo45teh6ku