دانلود رایگان مقاله مدل آب سطحی موجک گالرکین ناپیوسته تطبیقی

Abstract

This paper presents a Godunov-type numerical formulation that is local, conservative and scalable in both accuracy and resolution. The keystone of the framework is to recast a local multi-resolution discontinuous Galerkin formulation and, combine it with multiwavelets (MWDG) to adaptively determine local resolution level by manipulating multiwavelet coefficients driven by one threshold value set by the user. Recent advances in discontinuous Galerkin modelling of the shallow water equations with topography source term are directly transferred to the MWDG framework. The adaptive MWDG model is tested for simulation of transient and steady shallow flow test cases demonstrating ability to model compound flows with appropriate level resolutions, and with comparable predictive quality as uniform mesh counterpart corresponding to highest resolution available.

7. Conclusions

This work has presented an adaptive Godunov-type numerical framework for solving the shallow water equations with topography source term. The new numerical formulation combines the multiwavelets with the discontinuous Galerkin method to form the so-called MWDG merge. The appeal of the MWDG formulation is that it is locallyscalable for both accuracy and resolution scales. Another important feature of the MWDG framework is that it can be easily exploited to achieve dynamic grid resolution adaptivity from within the solution description and based on a single (threshold-value) parameter to sensibly achieve coarsening and refinement of resolution. The MWDG model has also been supported with features of relevance to conservative shallow flow modelling, i.e. a local and systematic slope limiting procedure, the Roe Riemann solver and piecewise polynomial well-balanced discretization to the topography source term, which have been found to be directly transferable from the standard RKDG method. Preliminary results (for a particular setting of the method with global third-order accuracy) reveal an excellent performance of the MWDG adaptive solution for two standard dam-break cases, under wet/wet and wet/dry conditions, and a steady transcritical flow with a shock over topography. The 2D extension of the MWDG framework to solve general homogeneous conservation laws is direct for structured quadrilateral grids [43]. For the case of the shallow water with source terms, the work is ongoing to enable modelling of terrain data and wet/dry fronts in an entirely consistent way with the discontinuous and convoluted nature of the 2D multiwavelet and scaling bases.