shunn_moin12

Summary

Verification of variable-density flow solvers using manufactured solutions. L. Shunn and P. Moin. Journal of Computational Physics, 231:3801-3827, 2012. (URL)

Abstract

The method of manufactured solutions (MMS) is used to verify the convergence properties of a low-Mach number, variable-density flow code. Three MMS problems relevant to combustion applications are presented and tested on a variety of structured and unstructured grids. Several issues are investigated, including the use of tabulated state properties (i.e., density) and the effect of sub-iterations in the time-advancement method. The MMS implementations provide a quantitative framework to evaluate the impact of these practices on the codes convergence and order-of-accuracy. Simulation results show that linear interpolation of the equation-of-state causes numerical fluctuations that impede convergence and reduce accuracy. Likewise, the sub-iterative time-advancement scheme requires a significant number of outer iterations to subdue splitting errors in highly nonlinear combustion problems. These findings highlight the importance of careful code and solution verification in the simulation of variable-density flows.

Bibtex entry

@ARTICLE { shunn_moin12,
    AUTHOR = { L. Shunn and P. Moin },
    TITLE = { Verification of variable-density flow solvers using manufactured solutions },
    JOURNAL = { Journal of Computational Physics },
    VOLUME = { 231 },
    PAGES = { 3801--3827 },
    YEAR = { 2012 },
    ABSTRACT = { The method of manufactured solutions (MMS) is used to verify the convergence properties of a low-Mach number, variable-density flow code. Three MMS problems relevant to combustion applications are presented and tested on a variety of structured and unstructured grids. Several issues are investigated, including the use of tabulated state properties (i.e., density) and the effect of sub-iterations in the time-advancement method. The MMS implementations provide a quantitative framework to evaluate the impact of these practices on the codes convergence and order-of-accuracy. Simulation results show that linear interpolation of the equation-of-state causes numerical fluctuations that impede convergence and reduce accuracy. Likewise, the sub-iterative time-advancement scheme requires a significant number of outer iterations to subdue splitting errors in highly nonlinear combustion problems. These findings highlight the importance of careful code and solution verification in the simulation of variable-density flows. },
    URL = { http://dx.doi.org/10.1016/j.jcp.2012.01.027 },
}