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WAMR: An adaptive wavelet method for the simulation of compressible reacting flow. Part I. Accuracy and efficiency of algorithm
The sparse grids produced by the WAMR method exhibit an impressive compression of the solution, reducing the number of collocation points used by factors of many orders of magnitude when compared to uniform grids of equivalent resolution. Expand
Discontinuous Galerkin Methods with Nodal and Hybrid Modal/Nodal Triangular, Quadrilateral, and Polygonal Elements for Nonlinear Shallow Water Flow
Abstract We present a comprehensive assessment of nodal and hybrid modal/nodal discontinuous Galerkin (DG) finite element solutions on a range of unstructured meshes to nonlinear shallow water flowExpand
Numerical solutions of multi-dimensional partial differential equations using an adaptive wavelet method
An adaptive wavelet method for the solution of timeindependent and time-dependent partial differential equations in d-dimensions based on d-dimensional interpolating wavelets constructed from tensor products of 1-D interpolatingWavelet amplitudes is described. Expand
Adaptive hierarchic transformations for dynamically p-enriched slope-limiting over discontinuous Galerkin systems of generalized equations
A family of generalized slope limiters in two dimensions for Runge-Kutta discontinuous Galerkin (RKDG) solutions of advection-diffusion systems are studied and a series of coupled p-enrichment schemes are introduced. Expand
A performance comparison of nodal discontinuous Galerkin methods on triangles and quadrilaterals
This work presents a study on the performance of nodal bases on triangles and on quadrilaterals for discontinuous Galerkin solutions of hyperbolic conservation laws. A nodal basis on triangles andExpand
Artificial boundary layers in discontinuous Galerkin solutions to shallow water equations in channels
In this work, we consider the application of Discontinuous Galerkin (DG) solutions to open channel flow problems, governed by two-dimensional shallow water equations (SWE), with solid curved wallExpand
A Comparison of Artificial Viscosity, Limiters, and Filters, for High Order Discontinuous Galerkin Solutions in Nonlinear Settings
This work uses a discontinuous Galerkin finite element method to study a nonlinear system of advection–diffusion–reaction equations and aspects of its regularity, and presents a family of solutions consisting of a sharp, computationally efficient slope limiter, a standard spectral filter, and a novel artificial diffusion algorithm with a solution-dependent entropy sensor. Expand
Adaptive Wavelet Method for Incompressible Flows in Complex Domains
An adaptive wavelet-based method provides an alternative means to refine grids according to local demands of the physical solution by using the Navier-Stokes-Brinkman equations to simulate flows over obstacles. Expand
Fully coupled methods for multiphase morphodynamics
Abstract We present numerical methods for a system of equations consisting of the two dimensional Saint–Venant shallow water equations (SWEs) fully coupled to a completely generalized ExnerExpand
High-order discontinuous Galerkin methods for coastal hydrodynamics applications
High-order discontinuous Galerkin finite element solutions of the shallow water equations to realistic coastal hydrodynamics problems to provide comparable accuracy to today’s state-of-the-art high-resolution, low-order coastal models at reduced computational expense. Expand