LAUSR

Abstract In this article, we start with the spatial dispersion difficulty encountered in the solution of physical phenomena controlled by partial differential equations. The one-dimensional diffusion phenomenon is taken as the research object, and the optimal precision that can be achieved under the theoretical grid number is obtained by programing. And a sensitivity analysis method for spatial discrete optimization with no analytical solution is proposed and evaluated. At the same time, this paper takes the non-adiabatic single-pore cavity of typical components in the research of aero engine air system network as an example, and applies the above method to the calculation of strong nonlinear fluid. We find that the optimal spatial discrete method obtained by applying the sensitivity method explored in this paper is at least seven times more efficient than the experience-based meshing method.