An adaptive mesh method for 1D hyperbolic conservation laws

Hu, Fuxing; Wang, Rong; Chen, Xueyong; Feng, Hui

doi:10.1016/j.apnum.2014.10.008

Cited by 12 publications

(4 citation statements)

References 36 publications

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“…A waveletbased adaptive WENO algorithm is constructed for Euler equations in [144]. A space-time adaptive ADER-WENO finite volume scheme is constructed in [65], and an adaptive mesh WENO method is developed in [104].…”

Section: Finite Difference and Finite Volume Weno Schemesmentioning

confidence: 99%

High order WENO and DG methods for time-dependent convection-dominated PDEs: A brief survey of several recent developments

Shu

2016

Journal of Computational Physics

161

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For solving time-dependent convection-dominated partial differential equations (PDEs), which arise frequently in computational physics, high order numerical methods, including finite difference, finite volume, finite element and spectral methods, have been undergoing rapid developments over the past decades. In this article we give a brief survey of two selected classes of high order methods, namely the weighted essentially non-oscillatory (WENO) finite difference and finite volume schemes and discontinuous Galerkin (DG) finite element methods, emphasizing several of their recent developments: bound-preserving limiters for DG, finite volume and finite difference schemes, which address issues in robustness and accuracy; WENO limiters for DG methods, which address issues in non-oscillatory performance when there are strong shocks, and inverse Lax-Wendroff type boundary treatments for finite difference schemes, which address issues in solving complex geometry problems using Cartesian meshes.

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Section: Finite Difference and Finite Volume Weno Schemesmentioning

confidence: 99%

High order WENO and DG methods for time-dependent convection-dominated PDEs: A brief survey of several recent developments

Shu

2016

Journal of Computational Physics

161

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“…Recently, an adaptive method is developed for solving one-dimensional systems of hyperbolic conservation laws, which combines the rezoning approach with the finite volume weighted essentially non-oscillatory scheme (Hua et al, 2015). They found this adaptive method exhibits more accurate resolution of discontinuities for a similar level of computational time comparing with that on a uniform mesh.…”

Section: Introductionmentioning

confidence: 99%

Dynamic adaptive finite element analysis of acoustic wave propagation due to underwater explosion for fluid-structure interaction problems

Emamzadeh

Ahmadi

Mohammadi

et al. 2015

J. Marine. Sci. Appl.

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In this paper, an investigation into the propagation of far field explosion waves in water and their effects on nearby structures are carried out. For the far field structure, the motion of the fluid surrounding the structure may be assumed small, allowing linearization of the governing fluid equations. A complete analysis of the problem must involve simultaneous solution of the dynamic response of the structure and the propagation of explosion wave in the surrounding fluid. In this study, a dynamic adaptive finite element procedure is proposed. Its application to the solution of a 2D fluid-structure interaction is investigated in the time domain. The research includes: a) calculation of the far-field scatter wave due to underwater explosion including solution of the time-depended acoustic wave equation, b) fluid-structure interaction analysis using coupled Euler-Lagrangian approach, and c) adaptive finite element procedures employing error estimates, and re-meshing. The temporal mesh adaptation is achieved by local regeneration of the grid using a time-dependent error indicator based on curvature of pressure function. As a result, the overall response is better predicted by a moving mesh than an equivalent uniform mesh. In addition, the cost of computation for large problems is reduced while the accuracy is improved.

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“…Over the years, adaptive zoning (also called adaptive moving mesh method or r-adaptivity) has been used to generate meshes that can help the numerical schemes to attain higher accuracy by producing a higher concentration of mesh points in regions of the domain where a higher resolution is desired [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16]. An efficient adaptive zoning is relevant for applications that need to model physical quantities characterized by steep gradients that propagate in space over time such as shock waves in a compressible medium.…”

Section: Introductionmentioning

confidence: 99%

A deep learning approach for adaptive zoning

Pasini¹,

Malenica²,

Chong³

et al. 2023

Preprint

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We propose a supervised deep learning (DL) approach to perform adaptive zoning on time dependent partial differential equations that model the propagation of 1D shock waves in a compressible medium. We train a neural network on a dataset composed of different static shock profiles associated with the corresponding adapted meshes computed with standard adaptive zoning techniques. We show that the trained DL model learns how to capture the presence of shocks in the domain and generates at each time step an adapted non-uniform mesh that relocates the grid nodes to improve the accuracy of Lax-Wendroff and fifth order weighted essentially non-oscillatory (WENO5) space discretization schemes. We also show that the surrogate DL model reduces the computational time to perform adaptive zoning by at least a 2x factor with respect to standard techniques without compromising the accuracy of the reconstruction of the physical quantities of interest.

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An adaptive mesh method for 1D hyperbolic conservation laws

Cited by 12 publications

References 36 publications

High order WENO and DG methods for time-dependent convection-dominated PDEs: A brief survey of several recent developments

High order WENO and DG methods for time-dependent convection-dominated PDEs: A brief survey of several recent developments

Dynamic adaptive finite element analysis of acoustic wave propagation due to underwater explosion for fluid-structure interaction problems

A deep learning approach for adaptive zoning

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