A low dissipation formulation for Weakly Compressible Riemann-Based SPH schemes

In the present work, a novel formulation aiming to reduce the numerical diffusion in Riemann-based weakly compressible SPH schemes is presented. Specifically, we propose scaling the diffusive term in the Riemann solver with the local Mach number. Notably, the proposed formulation is independent of any tuning parameter and can be used regardless of the specific approximate Riemann solver adopted in the scheme. Further, boundary conditions are enforced by adapting the modified dynamic boundary conditions (mDBC) from the open-source DualSPHysics solver applied to the one-sided Riemann problem. The proposed formulation is validated through Poiseuille flow, Taylor–Green vortices, lid-driven cavity flow, and impacting fluid patches test cases. Numerical results demonstrate that the new formulation increases accuracy, significantly reduces excessive numerical dissipation, and maintains an accurate pressure field even in highly dynamic impact flows.