Efficient implementation of volume/surface integrated average based multi-moment method

We investigated discretization strategies of the conservation equation in VSIAM3 (volume/surface integrated average based multi-moment method) which is a numerical framework for incompressible and compressible flows based on a multi-moment concept. We investigated these strategies through the lid-driven cavity flow problem, shock tube problems, 2D explosion test and droplet splashing on a superhydrophobic substrate. We found that the use of the CIP-CSLR (constrained interpolation profile-conservative semi-Lagrangian with rational function) method as the conservation equation solver is critically important for the robustness of incompressible flow simulations using VSIAM3 and that numerical results are sensitive to discretization techniques of the divergence term in the conservation equation. Based on these results, we proposed efficient implementation techniques of VSIAM3

Third-order less oscillatory and less diffusive compact stencil based upwind schemes, and their applications to incompressible flows and free surface flows

We propose novel third-order less oscillatory and less diffusive compact stencil based upwind schemes for the approximation of the continuity equation. The proposed schemes are based on the constrained interpolation profile-conservative semi-Lagrangian (CIP-CSL) schemes. An important feature of the proposed schemes is that the interpolation functions are constructed using only variables within one upwind cell (a cell average and two boundary values). Furthermore, the proposed schemes have third-order accuracy, and are also less oscillatory, less diffusive and fully conservative. The proposed schemes are validated through various benchmark problems and comparisons with experiments of two droplets collision/separation and droplet splashing. The numerical results have shown that the proposed schemes have third-order accuracy for smooth solution, and capture discontinuities and smooth solutions simultaneously without numerical oscillations. The proposed schemes can capture the secondary vorticity of lid-driven cavity flow of Re=7500 with a Cartesian grid of 64x64. The numerical results of two droplets collision/separation of We=40 show that the proposed schemes can reproduce droplets collision/separation with quite coarse grids. These numerical results of droplet splashing have demonstrated that proposed schemes can reduce numerical diffusions well against existing schemes and robust

An efficient multi-dimensional implementation of VSIAM3 and its applications to free surface flows

We propose an efficient multidimensional implementation of VSIAM3 (volume/surface integrated average-based multi-moment method). Although VSIAM3 is a highly capable fluid solver based on a multi-moment concept and has been used for a wide variety of fluid problems, VSIAM3 could not simulate some simple benchmark problems well (for instance, lid-driven cavity flows) due to relatively high numerical viscosity. In this paper, we resolve the issue by using the efficient multidimensional approach. The proposed VSIAM3 is shown to capture lid-driven cavity flows of the Reynolds number up to Re = 7500 with a Cartesian grid of 128 × 128, which was not capable for the original VSIAM3. We also tested the proposed framework in free surface flow problems (droplet collision and separation of We = 40 and droplet splashing on a superhydrophobic substrate). The numerical results by the proposed VSIAM3 showed reasonable agreements with these experiments. The proposed VSIAM3 could capture droplet collision and separation of We = 40 with a low numerical resolution (8 meshes for the initial diameter of droplets). We also simulated free surface flows including particles toward non-Newtonian flow applications. These numerical results have showed that the proposed VSIAM3 can robustly simulate interactions among air, particles (solid), and liquid