CFD code verification using least square extrapolation method

Least square extrapolation (LSE), a method for projecting numerically computed solutions of PDEs from multiple, coarser base grids onto a finer grid, improves solution accuracy by minimizing the residual of the discretized governing equations over the projected grid. In this work, the LSE technique is further developed for Navier-Stokes computations using finite volume formulation. The interplay between the concepts and the outcome of LSE, and the effects of solution gradients and singularities, nonlinear physics, and coupling of flow variables are investigated. It is demonstrated that LSE can help in code verification and offer quantitative measure for accuracy improvement. On the other hand, the existence of solution gradients or singularities can degrade the correlation between the residue of the governing equation and the solution error, which needs to be treated with special attention.