Development of Scalable Parallel Implicit Smoothed Particle Hydrodynamics using LAMMPS and Trilinos

We present a scalable parallel implementation of an Implicit Smoothed Particle Hydrodynamics (ISPH) method for incompressible flows. The Weakly Compressible SPH (WCSPH) method is the most commonly used SPH implementation for solving the compressible Navier Stokes (NS) equations. This conventional approach suffers from small time steps as dictated by the CFL condition, as well as from convergence issues introduced by the spatial discretization -- running WCSPH at larger scales to refine the discretization does not improve the quality of the solution. To address the small time step issue, we have implemented an implicit SPH method, where we use LAMMPS to provide the software infrastructure for particle simulations, and Trilinos solver packages to solve the linear systems needed for implicit time integration. To address the discretization issue, we use local correction tensors to achieve second order spatial convergence not possible in WCSPH. Due to these correction operators, the accuracy of solutions does not depend on the number of neighbors, which allows us to use a smaller set of neighbors. The code has been used to solve electro-kinetic flows, multi-phase flows, and porous media transport problems. Furthermore, the developed software framework is general and can be used for implicit time integration of other particle methods implemented in LAMMPS.