Comparison of two projection methods for modeling incompressible flows in MPM

Material point method (MPM) was originally introduced for large deformation problems in solid mechanics applications. Later, it has been successfully applied to solve a wide range of material behaviors. However, previous research has indicated that MPM exhibits numerical instabilities when resolving incompressible flow problems. We study Chorin's projection method in MPM algorithm to simulate material incompressibility. Two projection-type schemes, non-incremental projection and incremental projection, are investigated for their accuracy and stability within MPM. Numerical examples show that the non-incremental projection scheme provides stable results in single phase MPM framework. Further, it avoids artificial pressure oscillations and small time steps that are present in the explicit MPM approach.