An optimized dispersion–relation-preserving combined compact difference scheme to solve advection equations

Yu, Rena C.; Wang, Dan; He, Zhiguo; Pähtz, Thomas

doi:10.1016/j.jcp.2015.07.051

Cited by 16 publications

(7 citation statements)

References 41 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A distance function is applied at the interface, which is smoothed by solving the initialization equation [41]. The convection and diffusion terms in the transport equation are approximated using the upwinding combined compact difference (UCCD) algorithm [42,43]. The time integration for the transport equation is performed via a third-order Runge-Kutta (TVD-RK3) scheme [44] to calculate the particle concentration c'.…”

Section: Methodsmentioning

confidence: 99%

Investigations of dynamic behaviors of lock-exchange turbidity currents down a slope based on direct numerical simulation

Zhao

et al. 2018

Advances in Water Resources

View full text Add to dashboard Cite

Section: Methodsmentioning

confidence: 99%

Investigations of dynamic behaviors of lock-exchange turbidity currents down a slope based on direct numerical simulation

Zhao

et al. 2018

Advances in Water Resources

View full text Add to dashboard Cite

“…Accuracy issues regarding WENO schemes are discussed and improvements made in [96,57]. Efforts to improve the dissipation and / or dispersion properties of WENO schemes for high frequency wave computations are made in [241,180,161,107,118,260].…”

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

162

View full text Add to dashboard Cite

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.

show abstract

“…In order to eliminate this high-frequency oscillation, artificial viscosity should be included. Upwind compact schemes contain inherent artificial viscosity, which makes it more stable than centered compact schemes [24][25][26][27][28][29]. It should be noted, however, that, it may be premised that the introduced artificial viscosity should not be too large.…”

Section: Introductionmentioning

confidence: 99%

Numerical Study of Turbidity Current over a Three-Dimensional Seafloor

Yu¹,

Zhao²,

Wen³

et al. 2019

CiCP

View full text Add to dashboard Cite

Turbidity current over a Gaussian-bump is investigated numerically using the upwinding combined compact difference (UCCD) scheme and the immersed boundary (IB) method in Cartesian grids. In the prediction of lock-exchange gravity-driven flow motion, the initial discontinuous concentration field is smoothed to avoid numerical oscillation by solving the Hamilton-Jacobi equation. The UCCD spatial scheme with sixth-order accuracy which introduces less dispersion errors is then used to discretize advection and diffusion terms in the calculation of concentration transport equation. Direct forcing IB method is employed to treat solid object bumps in the fluid flow. The incompressible Navier-Stokes solutions are obtained through the projection method. Analysis of the smoothing procedure, grid sensitivity and the effect of the Schmidt numbers is performed for the turbidity current problem to validate the proposed numerical algorithm, which is shown to be capable of accurately demonstrating their results. Finally, several problems of turbidity current over a three-dimensional seafloor are investigated. The front locations of the currents interacting with the bump are predicted under different Reynolds numbers. Also, the current properties, namely the suspended particle mass, sedimentation rate and energy budget, are compared with the available numerical results.

show abstract

An optimized dispersion–relation-preserving combined compact difference scheme to solve advection equations

Cited by 16 publications

References 41 publications

Investigations of dynamic behaviors of lock-exchange turbidity currents down a slope based on direct numerical simulation

Investigations of dynamic behaviors of lock-exchange turbidity currents down a slope based on direct numerical simulation

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

Numerical Study of Turbidity Current over a Three-Dimensional Seafloor

Contact Info

Product

Resources

About