Effective Source Term Discretizations for Higher Accuracy Finite Volume Discretization of Parabolic Equations

Yaw Kyei

doi:10.31686/ijier.vol9.iss8.3305

Authors

Yaw Kyei North Carolina Central University https://orcid.org/0000-0001-8938-4730

DOI:

https://doi.org/10.31686/ijier.vol9.iss8.3305

Keywords:

Finite volume method, space-time control volume, local equation error expansion, her-order convergence, Heat equation, one-step scheme, numerical domain of dependence, general weighted quadratures, conservative flux integral

Abstract

A finite volume method is applied to develop space-time discretizations for parabolic equations based on an equation error method.
A space-time expansion of the local equation error based on flux integral formulation of the equation is first designed using a desired
framework of neighboring quadrature points for the solution and local source terms. The quadrature weights are then determined through a
minimization process for the error which constitutes all local compact fluxes about each centroid within the computational domain.
In utilizing a local source term distribution to account for diffusive fluxes, the right minimizing quadrature weights and collocation
points including subgrid points for the source terms may be determined and optimized for higher accuracies as well as robust higher-order
computational convergence. The resulting local residuals form a more complete description of the truncation errors which are then utilized
to assess the computational performances of the resulting schemes. The effectiveness of the discretization method is demonstrated by the
results and analysis of the schemes.

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Author Biography

Yaw Kyei, North Carolina Central University

Department of Decision Sciences

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