Multilayer open flow model: A simple pressure correction method for wave problems

Abstract

Summary This paper describes a pressure correction method for single‐ and multilayer open flow models. The method does not require any complex procedures to solve the discretization of the Poisson equation and is distinguished by a high computational efficiency. The algorithm can easily be adapted to irregular meshes and parallelized. Parabolic interpolation of the pressure profile is used for the free surface. The discretization of the Poisson equation is written in a matrix form, allowing its usage also in the case of basic function expansion of the depth pressure profile. The paper presents the results of algorithm verification where experimental data sensitive to the numerical dissipation of the calculation model was used. Iteration convergence is high including problems with dry‐bed flooding. The complete described technique of pressure correction is implemented in OpenCL on the GPU. Computation time for a test problem solved using CPU and GPU is compared.

Beyond Shallow Water: Appraisal of a numerical approach to hydraulic jumps based upon the Boundary Layer theory

“…The system (18) is composed of N equations of the type (19) and the solution is obtained by solving a trilinear system N xN . Note that the viscous step does not modify h. Equation (19) can be written as:…”

“…Mass exchanges between layers have also been considered [13,14,15]. From a numerical point of view, the global stability of weak solutions for the method proposed in [13] has been demonstrated in [16], while new efficient techniques have been recently developed [17,18,19]. Concerning applications beyond Newtonian fluids, a multilayer method with µ(I) rheology and side walls friction has also been derived [20].…”