Lagrangian Block Simulation of Buoyancy at Turbulence Interfaces

Abstract

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

A two-dimensional inviscid model of the gravity-current head by Lagrangian block simulation

“…The numerical error associated with the LBS is not cumulative, and false-diffusion error has been shown to be negligible by Chu and Altai [6]. A couple of simple advection experiments are given in the ''Appendix'' just to show how the LBS can capture discontinuities without the false diffusion and spurious oscillation errors.…”

“…1 Lagrangian block in the Eulerian cells a before and b after the advection and diffusion steps. The Lagrangian block simulation method and the notation details in this figure are given in Chu and Altai [6] Environ Fluid Mech (2018) 18:267-282 269…”

“…Tan and Chu [26,27] validated their LBS of wet water on dry bed by the exact analytical solution. Chu and Altai [4][5][6] compared their LBS of the laminar-and-turbulent interfaces with the experimental observations. In this paper, the numerical accuracy is assessed by the energy consideration in Sect.…”

“…Fluxes are not estimated so there are no numerical oscillation and diffusion errors from the truncation. Validation of the LBS method has been conducted in the calculation for the advance of wet water on dry bed by Tan and Chu [26,27] and in the simulations for the laminar-and-turbulent interfaces by Chu and Altai [4][5][6]. In the absence of spurious oscillations and false diffusion, the best possible inviscid model of the gravity-current head is constructed by the LBS.…”