Interface-preserving level set method for simulating dam-break flows - Gu, Z.H.; Wen, H.L.; Yu, C.H.; Sheu, Tony W.H. (Journal of computational physics, 2018)
•A three-dimensional interface-preserving level set method is developed in two steps to simulate dam break flow problems.•A DRP-CRWENO4 which achieves high-order accuracy with low dispersion error at smooth regions and switches to compact candidate stencils to avoid oscillations near discontinuities is developed.•Dam break flows are successfully simulated through the comparison of the predicted results with their corresponding experimental. An interface-preserving level set method that solves advection and re-initialization equations for simulating three-dimensional dam-break flows is developed. This method solves mass transfer problems on a uniform staggered Cartesian grid. The advection equation that is used to advect the level set function for capturing the interface is discretized by a proposed fourth-order spatial discretization scheme. This scheme is dispersion-relation-preserving and is compact-reconstruction weighted essentially non-oscillatory (DRP-CRWENO4). This scheme is compared with a previous fifth-order, weighted, essentially non-oscillatory (WENO5) scheme and can represent an interface more accurately, while exactly preserving mass conservation. This level set approach introduces a mass correction term into the re-initialization equation based on local interface-preserving conditions. An explicit Adams–Bashforth algorithm on a staggered Eulerian grid is used for the Navier–Stokes solver. The point successive over-relaxation method is then employed to solve the resulting linear system. Two one-dimensional wave propagation problems are simulated to verify the proposed DRP-CRWENO4 scheme, which is shown to be capable of effectively capturing large gradients with fourth-order accuracy. To demonstrate their resolution, the two advection schemes (WENO5 and DRP-CRWENO4) are applied in two two-dimensional benchmark cases, i.e., a vortex deforming problem and Zalesak's disk problem, where simulation results of both schemes are compared against each other. Demonstration study is then further extended to three-dimensional cases of the vortex deforming problem and Zalesak's sphere problem, and simulation results agree well with those using hybrid particle level set method. Finally, several dam-break problems with and without obstacles are investigated to validate the coupled two-phase incompressible flow and level set method solver. The results for the predicted flow structure and mass conservation properties are compared with the reported experimental data or numerical simulations.