Pure and Applied Mathematics Quarterly

Volume 14 (2018)

Number 1

Special Issue: In Honor of Chi-Wang Shu

Guest Editors: Jian-Guo Liu and Yong-Tao Zhang

V&V for turbulent mixing in the intermediate asymptotic regime

Pages: 193 – 222

DOI: https://dx.doi.org/10.4310/PAMQ.2018.v14.n1.a7

Authors

H. Zhang (Department of Applied Mathematics and Statistics, Stony Brook University, Stony Brook, New York, U.S.A.)

T. Kaman (Department of Mathematical Sciences, University of Arkansas, Fayetteville, Ark., U.S.A.)

D. She (Department of Applied Mathematics and Statistics, Stony Brook University, Stony Brook, New York, U.S.A.)

B. Cheng (Los Alamos National Laboratory, Los Alamos, New Mexico, U.S.A.)

J. Glimm (Department of Applied Mathematics and Statistics, Stony Brook University, Stony Brook, New York, U.S.A.)

D. H. Sharp (Los Alamos National Laboratory, Los Alamos, New Mexico, U.S.A.dcso@lanl.gov)

Abstract

Turbulent fluid flow interacts nonlinearly with a number of processes, including reactive flow (chemistry), radiation, and the transport of particles embedded in the flow. Subgrid scale modeling of these nonlinear processes is a major challenge to computational science. To this end, turbulent mixing of dissimilar fluids is a driver. Here we study validation issues for a class of turbulent mixing simulations. In previous work, we have obtained agreement between simulation and experiment. The present paper addresses a remaining issue, the role of meniscus related boundary effects for immiscible fluids in the validation process.

Validation and even verification has been controversial for turbulent mixing flows, as commonly used numerical models are diffusive and the resulting numerical diffusion modifies the parameters of the problem and its solution. Numerical diffusion of concentration and temperature is well documented in the scientific literature for Eulerian simulations. Lagrangian simulations, which might appear to avoid this problem, are subject to mesh tangling, ensuing regridding and use of Arbitrary Lagrangian Eulerian codes to substitute for a pure Lagrangian algorithm. In practice, Lagrangian methods are potentially subject to the same numerical diffusion issues when used to study complex interface instabilities.

Keywords

Rayleigh–Taylor instability, large eddy simulation, turbulent mixing

Full Text (PDF format)

We thank D. Youngs for calling the problem of meniscus and edge effects in immiscible experiments to our attention. Use of computational support by the Swiss National Supercomputing Centre is gratefully acknowledged. The work of Tulin Kaman was supported by Lawrence Jesser Toll, Jr. Endowed Chair of the Department of Mathematical Sciences in the J.William Fulbright College of Arts & Sciences at the University of Arkansas. Los Alamos National Laboratory Preprint LA-UR-18-22134. The paper contains material © British Crown Owned Copyright 2018/AWE.

Received 19 March 2018

Published 2 April 2019