Higher-Order Accurate Finite Volume Discretization of the Three-Dimensional Poisson Equation Based on An Equation Error Method

Yaw Kyei

doi:10.31686/ijier.vol6.iss6.1076

Authors

Yaw Kyei

North Carolina Central University, USA

DOI:

https://doi.org/10.31686/ijier.vol6.iss6.1076

Keywords:

Finite volume, local control volume, equation error expansion, uniform higherorder accurate convergence, local residual error, three-dimensional Poisson’s equation, local compact fluxes, flux integral formulation

Abstract

Efficient higher-order accurate finite volume schemes are developed for the threedimensional Poisson’s equation based on optimizations of an equation error expansion on local control volumes. A weighted quadrature of local compact fluxes and the flux integral form of the equation are utilized to formulate the local equation error expansions. Efficient quadrature weights for the schemes are then determined through a minimization of the error expansion for higher-order accurate discretizations of the equation. Consequently, the leading numerical viscosity coefficients are more accurately and completely determined to optimize the weight parameters for uniform higher-order convergence suitable for effective numerical modeling of physical phenomena. Effectiveness of the schemes are evaluated through the solution of the associated eigenvalue problem. Numerical results and analysis of the schemes demonstrate the effectiveness of the methodology.

Author Biography

Yaw Kyei, North Carolina Central University, USA

Department of Decision Sciences

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