Boundary condition enforcement for renormalised weakly compressible meshless Lagrangian methods

Abstract This paper introduces a boundary condition scheme for weakly compressible (WC) renormalised first-order accurate meshless Lagrangian methods (MLM) by considering both solid and free surface conditions. A hybrid meshless Lagrangian method-finite difference (MLM-FD) scheme on prescribed boundary nodes is proposed to enforce Neumann boundary conditions. This is used to enforce symmetry boundary conditions and the implied Neumann pressure boundary conditions on solid boundaries in a manner consistent with the Navier-Stokes equation leading to the accurate recovery of surface pressures. The free surface boundary conditions allow all differential operators to be approximated by the same renormalised scheme while also efficiently determining free surface particles. The boundary conditions schemes are implemented for two renormalised MLMs. A WC smoothed particle hydrodynamics (SPH) solver is compared to a WC generalised finite difference (GFD) solver. Applications in both 2D and 3D are explored. A substantial performance benefit was found when comparing the WCGFD solver to the WCSPH solver with the WCGFD solver realising a maximum speedup in the range of three times over WCSPH in both 2D and 3D configurations. The solvers were implemented in C++ and used the NVIDIA CUDA 10.1 toolkit for the parallelisation of the solvers.