On the Use of Commercial Finite Element Packages for a Dimensionless Solution to a Class of Problems

Physical laws provide a mathematical description of a physical phenomenon. The mathematical description is generally in the form of differential equations with appropriate initial and boundary conditions, called initial boundary value problems. The dimensionless form of an initial boundary value pro...

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Bibliographic Details
Published in:Computational and mathematical methods 2023, Vol.2023, p.1-15
Main Author: Pashah, S.
Format: Article
Language:English
Subjects:
Boundary conditions
Boundary value problems
Coding
Differential equations
Dimensional analysis
Dimensionless analysis
Engineering
Finite element analysis
Finite element method
Fluid dynamics
Formulations
Heat
Literature reviews
Material properties
Mathematical analysis
Numerical analysis
Packages
Shear stress
Software packages
Variables
Velocity
Citations: Items that this one cites
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Summary:Physical laws provide a mathematical description of a physical phenomenon. The mathematical description is generally in the form of differential equations with appropriate initial and boundary conditions, called initial boundary value problems. The dimensionless form of an initial boundary value problem is the first step for the solution to a class of problems. The approach is generally applied for closed-form (or analytical) solutions, whereas practical engineering problems can only be solved numerically. Commercial finite element packages are commonly used for the numerical solution of engineering problems with complexities caused by geometry, loading, and material properties. A numerical solution does not produce a formula; therefore, a completely new solution must be obtained even for minor changes in the data set. A single-dimensionless finite element analysis would solve a class of problems. Literature shows that user-developed finite element codes, not accessible for general use, are generally used for dimensionless finite element solutions. The availability of dimensionless analysis in a commercial finite element package would be very convenient. Commercial packages do not have built-in dimensionless formulations. However, all mainstream packages allow user-implemented formulation through different coding requirements. At least one researcher has used a commercial package for dimensionless analyses without coding. The work presents a guide on alternate implementation methods of dimensionless formulations in commercial packages. A sample case demonstrates the stepwise implementation of a dimensionless formulation without writing a customized finite element code.
ISSN:2577-7408
2577-7408
DOI:10.1155/2023/4839057