How can I formulate spectral methods for numerical computation?

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Discussion Overview

The discussion revolves around formulating spectral methods for numerical computation, specifically seeking references that provide worked examples and guidance on transitioning from governing equations to a computable form. The scope includes theoretical and applied aspects of numerical methods in fluid mechanics and heat transfer.

Discussion Character

  • Exploratory, Technical explanation, Homework-related

Main Points Raised

  • One participant requests references for spectral methods that include worked examples for numerical computation.
  • Another participant recommends "Computational Fluid Mechanics and Heat Transfer" by Pletcher et al. as a resource that includes derivations and applications related to spectral methods.
  • A follow-up inquiry seeks clarification on the specific edition and chapter of the recommended book, as the inquirer could not locate spectral methods in the glossary of the third edition.
  • A different participant mentions the fourth edition of the same book and suggests that spectral methods are discussed in the context of numerical methods applied to model equations, while also recommending chapter 13 of "Numerical Recipes" as an additional resource.

Areas of Agreement / Disagreement

Participants generally agree on the usefulness of the recommended books, but there is no consensus on the specific content related to spectral methods across different editions, as some participants have not found the information they seek.

Contextual Notes

Limitations include potential differences in content across editions of the recommended books and the lack of specific references to spectral methods in the editions reviewed by participants.

RobosaurusRex
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Hi,

I am new to spectral methods, does anyone have a good reference which shows some worked examples of formulating the method to be computed?
E.g. go from the general governing equations through transformation to the form which will be passed to a computer.

Cheers
 
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One of my go-to references for computational methods is Computational Fluid Mechanics and Heat Transfer by Richard H. Pletcher, John C. Tannehill, Dale Anderson. The book shows derivations and applications to different types of mass transfer problems and has a section on spectral methods. Maybe you can find a copy at your library.
 
NFuller said:
One of my go-to references for computational methods is Computational Fluid Mechanics and Heat Transfer by Richard H. Pletcher, John C. Tannehill, Dale Anderson. The book shows derivations and applications to different types of mass transfer problems and has a section on spectral methods. Maybe you can find a copy at your library.

Can you tell me which version of the book and which chapter you are referring to?
I have third edition and I cannot find spectral methods in the glossary.

Thanks for the quick reply.
 
I also have the fourth edition but I don't have the book on hand right now. From what I remember is was talked about in the Application of numerical methods to selected model equations. If it's not in there, another good resource on this is chapter 13 of Numerical Recipes.
 

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