A two-dimensional finite element recursion relation for the transport equation using nine-diagonal solvers. (1st September 2020)

• Record Type: Journal Article
• Authors: Pirbastami, Sogol; Pepper, Darrell W.
• Is Part Of: Numerical heat transfer. Volume 78:Number 3(2020)
• Page Start: 125
• Page End: 140
• Publication Date: 2020-09-01
• Subjects: Heat -- Transmission -- Measurement -- Periodicals; Mass transfer -- Measurement -- Periodicals; Numerical analysis -- Periodicals; Heat -- Transmission -- Periodicals; Mass transfer -- Periodicals; 621.4022
• DOI: 10.1080/10407790.2020.1777764
• Languages: English
• ISSNs: 1040-7790

Abstract

Abstract: A Galerkin-based finite element recursion relation is used to solve the heat transport equation in two-dimensions. The finite element method (FEM) is a powerful technique that is commonly used for solving complex engineering problems. However, the implementation of the FEM in multi-dimensional problems can be computationally expensive. A finite element recursion algorithm based on bilinear triangular, bilinear quadrilateral and quadratic Lagrangian approximations are employed to discretize the 2-D advection-diffusion equation. This algorithm is an extension of the 1-D Chapeau (linear element) technique, which employed a tridiagonal recursion expression common to the classical central finite-difference approach. The global matrix is nine-diagonal (for 2-D) and is solved using a modified strongly implicit procedure and a left-to-right sweep method.