Considerations about Using Truncation Method to Treat the Singularities when Solving with Higher Order Boundary Elements the Boundary Integral Equation of the Compressible Fluid Flow

摘要

This paper presents a numerical solution for the problem of the 2D compressible fluid flow around obstacles based on solving the singular boundary integral equation with quadratic boundary elements of lagrangean type. A truncation method is used to evaluate the coefficients that arise due to the singular integrals. The singular boundary equation obtained with the direct boundary element technique is considered in this paper. Some considerations about the truncation method are also made. A computer code in MATHCAD is created based on the method proposed. Numerical results are compared with exact ones for some particular cases when exact solutions exist. The comparisons show that even for a small numbers of nodes on the boundary the numerical solutions are in good agreement with the exact ones.