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A new 3D parallel SPH scheme for free surface flows. (English) Zbl 1242.76270
Summary: We propose a new robust and accurate SPH scheme, able to track correctly complex three-dimensional non-hydrostatic free surface flows and, even more important, also able to compute an accurate and little oscillatory pressure field. It uses the explicit third order TVD Runge-Kutta scheme in time, following [C.-W. Shu and S. Osher, J. Comput. Phys. 77, No. 2, 439–471 (1988; Zbl 0653.65072)] together with the new key idea of introducing a monotone upwind flux for the density equation, thus removing any artificial viscosity term. For the discretization of the velocity equation, the non-diffusive central flux has been used. A new flexible approach to impose the boundary conditions at solid walls is also proposed. It can handle any moving rigid body with arbitrarily irregular geometry. It does neither produce oscillations in the fluid pressure in proximity of the interfaces, nor does it have a restrictive impact on the stability condition of the explicit time stepping method, unlike the repellent boundary forces of [J.J. Monaghan, J. Comput. Phys. 110, No. 2, 399–406 (1994; Zbl 0794.76073)]. To asses the accuracy of the new SPH scheme, a 3D mesh-convergence study is performed for the strongly deforming free surface in a 3D dam-break and impact-wave test problem providing very good results.

76M28 Particle methods and lattice-gas methods
76D27 Other free boundary flows; Hele-Shaw flows
76D05 Navier-Stokes equations for incompressible viscous fluids
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