SPH-ALE Scheme for Weakly Compressible Viscous Flow with a Posteriori Stabilization

A highly accurate SPH method with a new stabilization paradigm has been introduced by the authors in recent paper aimed to solve Euler equations for ideal gases. We present here extension of viscous incompressible flow. Incompressibility is tackled assuming weakly compressible approach. The adopts SPH-ALE framework and improves accuracy taking high-order variable reconstruction Riemann states at midpoints between interacting particles. moving least squares technique used estimate derivatives required Taylor approximations convective fluxes, also provides needed discretize flux terms. Stability preserved implementing posteriori Multi-dimensional Optimal Order Detection (MOOD) procedure thus avoiding utilization any slope/flux limiter or artificial viscosity. capabilities are illustrated solving one- two-dimensional problems benchmark cases. proposed methodology shows improvements does not require parameter calibration. In addition, extended solution flow results validated analytical Taylor–Green, Couette Poiseuille flows, lid-driven cavity test