Finite Element Method vs. Integrated Finite Difference for Complex Geometries

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Discussion Overview

The discussion centers on comparing the finite element method (FE) and the integrated finite difference method (FD) for modeling flow in non-rectangular geometries. Participants explore the advantages and disadvantages of each method, particularly in the context of fluid modeling.

Discussion Character

  • Debate/contested
  • Technical explanation

Main Points Raised

  • One participant questions whether the finite element method is better, worse, or the same as the integrated finite difference method for non-rectangular geometries, citing concerns about flow field distortion with the FD method.
  • Another participant suggests that boundary element methods may offer significant advantages over both FE and FD methods for fluid modeling.
  • Concerns are raised about the FD method being an extrapolation method, which can lead to rapidly propagating errors under certain conditions, while the FE method is characterized as an interpolation method that may limit such issues.
  • Several participants share recommendations for literature that compares these methods, indicating a need for objective sources beyond competing group claims.

Areas of Agreement / Disagreement

Participants express differing views on the relative merits of the finite element and integrated finite difference methods, with no consensus reached regarding which method is superior for the discussed applications.

Contextual Notes

Participants acknowledge the need for objective comparisons and highlight the limitations of existing literature, which may be biased due to competing interests.

Who May Find This Useful

This discussion may be useful for researchers and practitioners in fluid dynamics, computational modeling, and numerical methods, particularly those evaluating different approaches for complex geometries.

bzz77
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Hello all:

For modeling flow (or whatever) in a non-rectangular geometry, can anyone comment on whether the finite element method would be better or worse or the same as the integrated finite difference method?

I'm reading some papers by competing groups (so I can decide which code to start using), and the finite element group maintains that the flow field can be distorted when using the integrated finite difference method.

My questions: first of all, is this true? If so, is the problem significant? And are there any other potential advantages/disadvantages of either method over the other?

I have basic knowledge of these methods, but not enough to evaluate their advantages/disadvantages in a meaningful way! Thanks.
 
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For fluid modelling, boundary element methods often have significant calculation advantage over either FE or FD methods.

The problem with a FD method is that it is an extrapolation method for which errors can rapidly propagate and grow in the wrong circumstances.


The FE method is an interpolation method which limits this problem

go well
 
Last edited:


Thanks Studiot. I'll look into that.

Right now my choice is between integrated finite difference and finite element though. Thanks again.
 


For the FD method I can recommend

Numerical Solution of Partial Differential Equations: Finite Difference Methods

GD Smith

Oxford
 


Thanks a lot, Studiot.
 


Further bibliography

Brebbia has written several books about the boundary element method, including comparisons with FE/FD, working problems both ways.

Boundary elements for engineers

Elements of Computational Hydraulics by

Koutitas

Compares both FD and FE methods with many practical examples.
 


Thanks again for going to so much trouble, Studiot. I'll definitely look that up. So far the only comparisons of FE and integrated FD I can find are by the competing groups, and I need something objective. Appreciate it.
 

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