Journal ArticleDOI
Towards parallel WENO wavelet methods for the simulation of compressible two-fluid models
TLDR
In this article , a parallel formulation of a WENO multiresolution scheme based on OpenMP has been proposed, which has the capability of accurately capturing the formation of shocks and the evolution of rarefaction waves.Abstract:
In the current work a seven-equation model of two-dimensional two-phase flow problems is analyzed by a parallel formulation of a WENO multiresolution scheme. The scheme adaptivity is obtained by a third order interpolating wavelet transform associated to a threshold operator. In this way, a sparse representation of the vector solution is obtained at each time step. The evolution in time is performed by a third order TVD Runge-Kutta scheme. For the spatial integration on the sparse grid, the Lax-Friedrich flux splitting scheme is considered in which the flux derivatives are approximated by the standard fifth-order WENO scheme. The parallel formulation of the code is based on OpenMP, which is crucial for the computation of long term simulations with shorter computational times. The considered adaptive parallel WENO scheme has the capability of accurately capturing the formation of shocks and the evolution of rarefaction waves, as evinced by the presented numerical simulations. read more
Citations
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Journal ArticleDOI
GPU-parallelisation of Haar wavelet-based grid resolution adaptation for fast finite volume modelling: application to shallow water flows
TL;DR: In this paper , a GPU-parallelized Haar wavelet multiresolution analysis (MRA) model (GPU-HWFV1) is proposed to solve the problem of parallel tree traversal.
GPU-parallelisation of wavelet-based grid adaptation for fast finite volume modelling: application to shallow water flows
TL;DR: In this article , a GPU-parallelized Haar wavelet model (GPU-HWFV1) was proposed to reduce the computational cost of the MRA by applying Z-order space-filling curves and adopting a parallel tree traversal algorithm.
References
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Journal ArticleDOI
Total variation diminishing Runge-Kutta schemes
Sigal Gottlieb,Chi-Wang Shu +1 more
TL;DR: A class of high order TVD (total variation diminishing) Runge-Kutta time discretization initialized in Shu& Osher (1988), suitable for solving hyperbolic conservation laws with stable spatial discretizations is explored, verifying the claim that TVD runge-kutta methods are important for such applications.
Book
Adaptive mesh refinement for hyperbolic partial differential equations
Marsha Berger,Joseph Oliger +1 more
TL;DR: This work presents an adaptive method based on the idea of multiple, component grids for the solution of hyperbolic partial differential equations using finite difference techniques based upon Richardson-type estimates of the truncation error, which is a mesh refinement algorithm in time and space.
Book
Advanced Numerical Approximation of Nonlinear Hyperbolic Equations
B. Cockburn,Centro internazionale matematico estivo,Centro internazionale matematico estivo. Session +2 more
TL;DR: In this article, the Discontinuous Galerkin method for convection-dominated problems is used to approximate solutions of nonlinear conservation laws and adaptive finite element methods for conservation laws.
Journal ArticleDOI
The Riemann problem and a high-resolution Godunov method for a model of compressible two-phase flow
TL;DR: Numerical results are presented, demonstrating the accuracy of the numerical method and in particular, the accurate numerical description of the flow in the vicinity of a solid contact where phases couple and nozzling terms are important.
Journal ArticleDOI
The Riemann problem for the Baer-Nunziato two-phase flow model
TL;DR: In this article, the Riemann problem for the two-phase flow model was investigated and the exact solution for it was constructed for the Baer-Nunziato model.