Volume 11, Issue 1
A Preconditioned Implicit Free-Surface Capture Scheme for Large Density Ratio on Tetrahedral Grids

Xin Lv, Qingping Zou, D. E. Reeve & Yong Zhao

Commun. Comput. Phys., 11 (2012), pp. 215-248.

Published online: 2012-11

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  • Abstract

We present a three dimensional preconditioned implicit free-surface capture scheme on tetrahedral grids. The current scheme improves our recently reported method [10] in several aspects. Specifically, we modified the original eigensystem by applying a preconditioning matrix so that the new eigensystem is virtually independent of density ratio, which is typically large for practical two-phase problems. Further, we replaced the explicit multi-stage Runge-Kutta method by a fully implicit Euler integration scheme for the Navier-Stokes (NS) solver and the Volume of Fluids (VOF) equation is now solved with a second order Crank-Nicolson implicit scheme to reduce the numerical diffusion effect. The preconditioned restarted Generalized Minimal RESidual method (GMRES) is then employed to solve the resulting linear system. The validation studies show that with these modifications, the method has improved stability and accuracy when dealing with large density ratio two-phase problems.


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@Article{CiCP-11-215, author = {}, title = {A Preconditioned Implicit Free-Surface Capture Scheme for Large Density Ratio on Tetrahedral Grids}, journal = {Communications in Computational Physics}, year = {2012}, volume = {11}, number = {1}, pages = {215--248}, abstract = {

We present a three dimensional preconditioned implicit free-surface capture scheme on tetrahedral grids. The current scheme improves our recently reported method [10] in several aspects. Specifically, we modified the original eigensystem by applying a preconditioning matrix so that the new eigensystem is virtually independent of density ratio, which is typically large for practical two-phase problems. Further, we replaced the explicit multi-stage Runge-Kutta method by a fully implicit Euler integration scheme for the Navier-Stokes (NS) solver and the Volume of Fluids (VOF) equation is now solved with a second order Crank-Nicolson implicit scheme to reduce the numerical diffusion effect. The preconditioned restarted Generalized Minimal RESidual method (GMRES) is then employed to solve the resulting linear system. The validation studies show that with these modifications, the method has improved stability and accuracy when dealing with large density ratio two-phase problems.


}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.170510.290311a}, url = {http://global-sci.org/intro/article_detail/cicp/7359.html} }
TY - JOUR T1 - A Preconditioned Implicit Free-Surface Capture Scheme for Large Density Ratio on Tetrahedral Grids JO - Communications in Computational Physics VL - 1 SP - 215 EP - 248 PY - 2012 DA - 2012/11 SN - 11 DO - http://dor.org/10.4208/cicp.170510.290311a UR - https://global-sci.org/intro/article_detail/cicp/7359.html KW - AB -

We present a three dimensional preconditioned implicit free-surface capture scheme on tetrahedral grids. The current scheme improves our recently reported method [10] in several aspects. Specifically, we modified the original eigensystem by applying a preconditioning matrix so that the new eigensystem is virtually independent of density ratio, which is typically large for practical two-phase problems. Further, we replaced the explicit multi-stage Runge-Kutta method by a fully implicit Euler integration scheme for the Navier-Stokes (NS) solver and the Volume of Fluids (VOF) equation is now solved with a second order Crank-Nicolson implicit scheme to reduce the numerical diffusion effect. The preconditioned restarted Generalized Minimal RESidual method (GMRES) is then employed to solve the resulting linear system. The validation studies show that with these modifications, the method has improved stability and accuracy when dealing with large density ratio two-phase problems.


Xin Lv, Qingping Zou, D. E. Reeve & Yong Zhao. (2020). A Preconditioned Implicit Free-Surface Capture Scheme for Large Density Ratio on Tetrahedral Grids. Communications in Computational Physics. 11 (1). 215-248. doi:10.4208/cicp.170510.290311a
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