I come from a computer graphics background without any professional in computational science. But I find my job(game engine development) being related to this field. May I ask some general questions about computational science?

Last year, we made a product for deformable object(such as hair, cloth, etc.) simulation. It is said to be a successful product since it can produce really convincing result in most of the time.

However I find it difficult to state clearly which physics model is adopted, and which computation method is applied. When our users doubt whether a simulation result they get is incorrect, I cannot assure even I am a author of this product.

Does our physics model adopted lead to this result? Does our computational method work correctly so that it converges to our physics model? I do not know.

And in these days, while I am doing some research in SPH(Smoothed-particle hydrodynamics) simulation, I cannot understand how those parameters are chosen. When I see a simulation result, I am not sure if there is a bug in my code, or if this result is compliant with the physics model.

Finally I think I can describe my confuse in following questions:

  • How can I check a simulation result is compliant with the physics model? How can I know a computation method applied in our program(like discretion or truncation of a continuous model) behaves well?

  • Is there any introductory book/paper/online course on the whole process from physics model derivation to computation method design and error analysis?

  • $\begingroup$ Hi @TheBusy Typist and welcome to scicomp! Your question is very interesting, but there is a problem with it. The update expands the scope of the question rather than narrowing it. I realize there are multiple related issues/questions that you face, but it's better to post each question individually. $\endgroup$ – Paul Sep 14 '14 at 18:40
  • 1
    $\begingroup$ Agreed. It's better to split up your one long question into multiple self-contained questions. You'll get better answers, and people are more likely to answer those questions because short questions are easier to read. $\endgroup$ – Geoff Oxberry Sep 15 '14 at 3:27
  • $\begingroup$ Thank you for advice. I will remove the update and leave this question in its general form. Actually I am satisfy with the answer I get. I will accept it soon. I think I will take more time to make the question targeting a specific physics model more clear and post a new question. $\endgroup$ – TheBusyTypist Sep 15 '14 at 4:32

The first question deals with what is called consistency and convergence. It states that when you reduce your time and spatial discretizations, your solution, in the limit, goes towards the analytical solution. If you use standard, well-known methods this is usually given. If you design your own method you need to verify this yourself by symbolically taking the limit of your method as your steps shrink and ensure that the original equations are recovered. This is very much in the realm of numerical analysis.

Another part of the question involves whether your continuous equations properly describe the physics. This portion is the actual modelling. To answer whether your equations are sufficient you need to have a good understanding of what you want from your simulations. Again, unless you are coming up with your own equations, the parameters for which certain equations reproduce real world physics well are usually part of the presentation of the equation. Look back to the original source to see what the equation was designed for.

Finally, your request for reference is still very broad. You could fill a small library with the textbooks that have been written on the subjects of numerical analysis and physics modelling . If you want to refine your question to ask about specific physical phenomenon or certain types of numerical techniques, we may be able to point you to more canonical references for them.

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