Minimal intervention to simulations of shallow-water equations

Pinilla, Camilo E.; Bouhairie, Salem; Tan, Lai Wai; Chu, Vincent H.

doi:10.1016/j.jher.2009.10.005

Cited by 9 publications

(4 citation statements)

References 18 publications

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“…The rate of h (i,j) for advancing h n ði;jÞ to h ðn þ 1Þ ði;jÞ according to the continuity equation is: The rate of q y(i,j) according to the y-momentum equation is: This numerical model is an improved version of the numerical scheme by Pinilla et al (2010).…”

Section: Advance In Time By the Runge-kutta Methodsmentioning

confidence: 99%

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High-order interpolation schemes for shear instability simulations

Ghannadi

Chu

2015

Int Jnl of Num Meth for HFF

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Purpose -The purpose of this paper is to evaluate the performance of a numerical method for the solution to shallow-water equations on a staggered grid, in simulations for shear instabilities at two convective Froude numbers. Design/methodology/approach -The simulations start from a small perturbation to a base flow with a hyperbolic-tangent velocity profile. The subsequent development of the shear instabilities is studied from the simulations using a number of flux-limiting schemes, including the second-order MINMOD, the third-order ULTRA-QUICK and the fifth-order WENO schemes for the spatial interpolation of the nonlinear fluxes. The fourth-order Runge-Kutta method advances the simulation in time. Findings -The simulations determine two parameters: the fractional growth rate of the linear instabilities; and the vorticity thickness of the first nonlinear peak. Grid refinement using 32, 64, 128, 256 and 512 nodes over one wave length determines the exact values by extrapolation and the computational error for the parameters. It also determines the overall order of convergence for each of the flux-limiting schemes used in the numerical simulations. Originality/value -The four-digit accuracy of the numerical simulations presented in this paper are comparable to analytical solutions. The development of this reliable numerical simulation method has paved the way for further study of the instabilities in shear flows that radiate waves.

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Section: Advance In Time By the Runge-kutta Methodsmentioning

confidence: 99%

“…The strategy developed for the thirdorder QUICK was ULTRA-QUICK. Pinilla et al (2010) formalized the flux-limiting strategy using the DWF and NV for two-dimensional (2D) simulations on a staggered grid.…”

Section: Flux-limiting Schemesmentioning

confidence: 99%

High-order interpolation schemes for shear instability simulations

Ghannadi

Chu

2015

Int Jnl of Num Meth for HFF

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“…Due to numerical oscillations at the advancing front, and the possibility of negative water depth, breakdown of computations would occur using the FV method without the flux limiter to manage the numerical oscillations (Pinilla et al, 2008). However, this difficulty is resolved when blocks are used as the computational elements.…”

Section: Introductionmentioning

confidence: 99%

Wave runup simulations using Lagrangian blocks on Eulerian mesh

Tan

Chu

2010

Journal of Hydro-environment Research

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“…Diffusion often is introduced synthetically in many schemes to gain computational stability. Occasional switching to a diffusive upwind scheme is one classic strategy to manage the numerical oscillations [1,2,3,4,5]. Lagrangian block simulation (LBS) offers an alternative that could eliminate the spurious numerical oscillations and false diffusive error [6,7].…”

mentioning

confidence: 99%

Lagrangian Block Simulation of Buoyancy at Turbulence Interfaces

Chu

Altai

2015

Comput Thermal Scien

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Simulations of turbulent interfaces produced by positive and negative buoyancy are conducted by moving blocks of fluid in the direction of the flow. The second moment of the blocks increases at a rate proportional to the diffusivity. The block simulation is free of numerical oscillations. Unlike most classical methods, the error associated with Lagrangian block simulation is not cumulative. Artificial diffusion error is negligible. The non-diffusive Lagrangian block simulations have provided reliable data to evaluate the performance of (i) sub-grid scale modelling and (ii) K-ε modelling of turbulent flow under the opposing influence of buoyancy. INTRODUCTIONMost computational fluid-dynamics codes are developed using the Eulerian description. To find the numerical solution, fluxes are estimated on the surface of the finite volume using a truncation series. Spurious numerical oscillations and artificial numerical diffusion are consequences, particularly in regions across flow discontinuities. Diffusion often is introduced synthetically in many schemes to gain computational stability. Occasional switching to a diffusive upwind scheme is one classic strategy to manage the numerical oscillations [1,2,3,4,5]. Lagrangian block simulation (LBS) offers an alternative that could eliminate the spurious numerical oscillations and false diffusive error [6,7]. The blocks move in the direction of the flow. The squares of the block widths expand in proportion to the diffusivities. The block simulation procedure consists of three steps: (i) Lagrangian advection and diffusion, (ii) division into portions, and (iii) reassembly of the portions into new blocks. The blocks are renewed in each time increment to prevent excessive distortion. In this paper simulation of buoyancy at turbulence interfaces has been carried out using the LBS method. In one series of simulations, the Kelvin-Helmholtz instabilities initiate turbulence across

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Minimal intervention to simulations of shallow-water equations

Cited by 9 publications

References 18 publications

High-order interpolation schemes for shear instability simulations

High-order interpolation schemes for shear instability simulations

Wave runup simulations using Lagrangian blocks on Eulerian mesh

Lagrangian Block Simulation of Buoyancy at Turbulence Interfaces

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