Local singular boundary method for two-dimensional steady and unsteady potential flow

Abstract This paper focuses on deriving a local variant of a singular boundary method for steady and unsteady potential flow. Compared to the global variant, local leads to the sparse resulting matrix of the system of equations and thus makes the solution of large-scale tasks more effective. The combination of the singular boundary method and the finite collocation method were used for localization. The article compares the results of global and local variation on several examples for both steady and unsteady flow, and the dependence of the solution precision on the density of the nodal network and the dimensions of the stencil was also studied.