TURBULENCE INTERFACE SIMULATION BY LAGRANGIAN BLOCKS

Abstract:

Most 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, for example, is one classic strategy to manage the numerical oscillations [see e.g., Ghannadi & Chu 2015].

Lagrangian-block simulation offers an alternative that could minimize the spurious oscillations and false diffusive error. 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 (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. Details of the Lagrangian-block simulations method have been given in a series of papers by Tan & Chu (2012), Chu & Altai (2012, 2015}.

In this paper, the exchanges across turbulence interfaces are considered for two problems. The first series of the simulations are conducted to find the mass and momentum exchanges across a shallow flow of two different depth. In the simulations, the advection and diffusion of three separated systems of blocks that contain the mass, momentum and potential vorticity are carried out using the Lagrangian-block simulation method. The simulation results are compared with data obtained from a previous laboratory investigation and related to the shear instability problem in rotating shear flow previously considered by Chu (2014). The second problem involves the turbulence generation across the interface of an internal waves. The simulation shows the development of gravitational stable interface in part of the interface and the overturning in another part of the unstable interface. The process is not quantitative known until the compilation of results obtained from the present Lagrangian-block simulation. The development of the interface however is of great significance to many geo-environmental applications.