A Two-Dimensional Finite Element Recursion Relation for the Transport Equation Using Nine-Diagonal Solvers
Document Type
Article
Publication Date
6-22-2020
Publication Title
Numerical Heat Transfer, Part B: Fundamentals
First page number:
1
Last page number:
17
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.
Disciplines
Engineering | Mechanical Engineering
Language
English
Repository Citation
Pirbastami, S.,
Pepper, D. W.
(2020).
A Two-Dimensional Finite Element Recursion Relation for the Transport Equation Using Nine-Diagonal Solvers.
Numerical Heat Transfer, Part B: Fundamentals
1-17.
http://dx.doi.org/10.1080/10407790.2020.1777764