International Journal for Numerical Methods in Fluids

In this paper, we present a computationally efficient semi-implicit scheme for the simulation of hydrostatic three-dimensional free surface flow problems on staggered unstructured Voronoi meshes. A piecewise high-order polynomial vector velocity field is then reconstructed from the scalar normal velocities at the cell faces by using a high-order constrained least-squares reconstruction operator. The reconstructed high-order piecewise polynomial velocity field is used for trajectory integration in a semi-Lagrangian approach to discretize the nonlinear convective terms. For that purpose, a high-order Taylor method is used as ODE integrator. The resulting semi-implicit algorithm is validated on a set of academic test problems and is finally applied to a real-world engineering problem consisting of a curved channel of a hydroelectric power plant.

The present paper extends an established Riemann-based finite volume hydrocode for compressible pure water to admit change of phase. Closure of the equation set is achieved by deriving equations of state for pure fluids and the mixture that cover all possible fluid states. Calculations include a one dimensional cavitation tube; one dimensional condensation front; collapse of a cavitation bubble in water in one dimension; and, unsteady two-dimensional hypervelocity flow past a cavitating hydrofoil.

The paper describes a combination of a preconditioning method with a high-order compact scheme for the purpose of solving the compressible Navier–Stokes equations in moderate and low Mach number regimes. Combined with characteristic boundary conditions, the proposed approach is robust and very efficient from the point of view of convergence and accuracy. The computations were performed in typical benchmark cases including the Burggraf flow, the flow over a backward facing step, and in 2D and 3D shear-driven cavities.

This is the first work to apply stencil adaptive technique with the phase field-lattice Boltzmann method to simulate multiphase flows.

In this work, we replace the rezoning phase of classical ALE method by a rezoning where we allow the connectivity between cells of the mesh to change. This leads to a polygonal mesh that recovers the Lagrangian features in order to follow more efficiently the flow. Those reconnections allow to deal with complex geometries and high vorticity problems contrary to the ALE method. For optimizing the remapping phase, we have modified the idea of swept-integration-based method. The new method used here is called swept-intersection-based remapping method.