Finite volume and pseudo-spectral schemes for the fully nonlinear 1D Serre equations

After we derive the Serre system of equations of water wave theory from a generalized variational principle, we present some of its structural properties. We also propose a robust and accurate finite volume scheme to solve these equations in one horizontal dimension. The numerical discretization is validated by comparisons with analytical, experimental data or other numerical solutions obtained by a highly accurate pseudo-spectral method.Comment: 28 pages, 16 figures, 75 references. Other author's papers can be downloaded at http://www.denys-dutykh.com

The VOLNA code for the numerical modelling of tsunami waves: generation, propagation and inundation

A novel tool for tsunami wave modelling is presented. This tool has the potential of being used for operational purposes: indeed, the numerical code \VOLNA is able to handle the complete life-cycle of a tsunami (generation, propagation and run-up along the coast). The algorithm works on unstructured triangular meshes and thus can be run in arbitrary complex domains. This paper contains the detailed description of the finite volume scheme implemented in the code. The numerical treatment of the wet/dry transition is explained. This point is crucial for accurate run-up/run-down computations. Most existing tsunami codes use semi-empirical techniques at this stage, which are not always sufficient for tsunami hazard mitigation. Indeed the decision to evacuate inhabitants is based on inundation maps which are produced with this type of numerical tools. We present several realistic test cases that partially validate our algorithm. Comparisons with analytical solutions and experimental data are performed. Finally the main conclusions are outlined and the perspectives for future research presented.Comment: 47 pages, 27 figures. Other author's papers can be downloaded at http://www.lama.univ-savoie.fr/~dutykh

Turbulence Model Implementation and Verification in the SENSEI CFD Code

This paper outlines the implementation and verification of the negative Spalart-Allmaras turbulence model into the SENSEI CFD code. The SA-neg turbulence model is implemented in a flexible, object-oriented framework where additional turbulence models can be easily added. In addition to outlining the new turbulence modeling framework in SENSEI, an overview of the other general improvements to SENSEI is provided. The results for four 2D test cases are compared to results from CFL3D and FUN3D to verify that the turbulence models are implemented properly. Several differences in the results from SENSEI, CFL3D, and FUN3D are identified and are attributed to differences in the implementation and discretization order of the boundary conditions as well as the order of discretization of the turbulence model. When a solid surface is located near or intersects an inflow or outflow boundary, higher order boundary conditions should be used to limit their effect on the forces on the surface. When the turbulence equations are discretized using second order spatial accuracy, the edge of the eddy viscosity profile seems to be sharper than when a first order discretization is used. However, the discretization order of the turbulence equation does not have a significant impact on output quantities of interest, such as pressure and viscous drag, for the cases studied