On the accuracy assessment of Laplacian models in MPS

From the basis of the Gauss divergence theorem applied on a circular control volume that was put forward by Isshiki (2011) in deriving the MPS-based differential operators, a more general Laplacian model is further deduced from the current work which involves the proposal of an altered kernel function. The Laplacians of several functions are evaluated and the accuracies of various MPS Laplacian models in solving the Poisson equation that is subjected to both Dirichlet and Neumann boundary conditions are assessed. For regular grids, the Laplacian model with smaller N$N$ is generally more accurate, owing to the reduction of leading errors due to those higher-order derivatives appearing in the modified equation. For irregular grids, an optimal N$N$ value does exist in ensuring better global accuracy, in which this optimal value of N$N$ will increase when cases employing highly irregular grids are computed. Finally, the accuracies of these MPS Laplacian models are assessed in an incompressible flow problem.