No abstract

In order to solve complex problems in hydrodynamics, a new method is developed. This method aims at finding a good compromise between computational efficiency, accuracy, and easy handling of complex geometries. The chosen method is an Explicit Cartesian Finite Volume method for Hydrodynamics (ECFVH) based on a compressible (hyperbolic) solver, with an embedded method for interfaces and geometry handling. The explicit nature of the solver is obtained through a weakly-compressible approach chosen to simulate nearly-incompressible flows. The explicit cell-centered resolution allows for an efficient solving of very large simulations together with a straightforward handling of multi-physics. The use of an embedded Cartesian grid ensures accuracy and efficiency, but also implies the need for a specific treatment of complex solid geometries, such as the cut-cell method in the fixed or moving body frame. Robustness of the cut-cell method is ensured by specific procedures to circumvent small cell volume numerical errors. A characteristic flux method for solving the hyperbolic part of the Navier-Stokes equations is used for which upwinding is necessary, also introducing numerical viscosity. This numerical viscosity is evaluated before trying to model viscous and turbulent effects. In a first approach viscous effects are computed via a finite difference Laplacian operator introduced as a source term. This solver is validated on 2-D test cases and future improvements are discussed.

In order to efficiently address complex problems in hydrodynamics, the advances in the development of a new method are presented here. This method aims at finding a good compromise between computational efficiency, accuracy, and easy handling of complex geometries. The chosen method is an Explicit Cartesian Finite Volume method for Hydrodynamics (ECFVH) based on a compressible (hyperbolic) solver, with a ghost-cell method for geometry handling and a Level-set method for the treatment of biphase-flows. The explicit nature of the solver is obtained through a weakly-compressible approach chosen to simulate nearly-incompressible flows. The explicit cell-centered resolution allows for an efficient solving of very large simulations together with a straightforward handling of multi-physics. A characteristic flux method for solving the hyperbolic part of the Navier-Stokes equations is used. The treatment of arbitrary geometries is addressed in the hyperbolic and viscous framework. Viscous effects are computed via a finite difference computation of viscous fluxes and turbulent effects are addressed via a Large-Eddy Simulation method (LES). The Level-Set solver used to handle biphase flows is also presented. The solver is validated on 2-D test cases (flow past a cylinder, 2-D dam break) and future improvements are discussed.

An explicit Finite Volume method for solving hydrodynamic flows is presented in this paper. These developments are based on an explicit cell-centered scheme solving the compressible fluid equations in a pseudo-compressible strategy where second-order accuracy is provided by using a MUSCL scheme together with various limiters for the hyperbolic part. In this recent model, boundaries are handled through a Cut-Cell method, so that solids as well as fluid interfaces are explicitly moved in a non-diffusive way, ensuring local mass conservation within fluids. An improved cut-cell algorithm based on the Voxel traversal algorithm coupled with a local Floodfill Scanline has been developed, in order to handle boundaries of arbitrary geometrical complexity. To cope with small cells instability problems near the boundaries, a fully conservative merging method is implemented. In this paper, this solver is validated on 2-D hydrodynamic test cases, such as flows past obstacles. Test cases involving large body movement are then performed and discussed. The latter test cases are performed both in the frame of the body and in a fixed frame where the body is moving across the grid. Then, a two-fluid formulation is introduced in the model and described in detail in the present paper. First validations of this two-fluid formulation are eventually presented.