How to modify source term

[Kadir Çar]

I have a special conservation law model which is of the form of balance law(it includes some nonlinear source terms)  in 1D. I would like to know where I can modify the source term by using finite volume method. (There are examples using ODE/ implicit euler method but thats not useful for us).

p.s. my source term doesn't include partial derivative terms, we have only nonlinear terms

[David Ketcheson]

I'm not sure what you mean by "where I can modify the source term".  But for PyClaw source term implementation is discussed here, with a link to an example: https://www.clawpack.org/pyclaw/problem.html#adding-source-terms.

[Kadir Çar]

Thanks for your reply, I have tried to edit the source terms in the src1.f file but the problem is, as I have said earlier I couldn't find any nonlinear source term in any examples or in any documentation. I am trying to handle that problem. 

David Ketcheson <dke...@gmail.com>, 18 Eki 2024 Cum, 20:07 tarihinde şunu yazdı:

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[David Ketcheson]

It's always helpful to specify which package you are using.  The documentation I linked is for PyClaw but it sounds like you are using one of the other packages.  There is an example for instance in 

clawpack/classic/examples/acoustics_2d_radial/1drad/

You say that "my source term doesn't include partial derivative terms", in which case your source term is an ODE.  So I don't understand why you say ODE source term examples aren't useful.  I think you'll need to provide more clear information to get more help.

[Randall J LeVeque]

To clarify why it's an ODE being solved, the fractional step approach taken in Clawpack is to split

  q_t + f(q)_x = psi(q)

into a step with the homogeneous conservation law

   q_t + f(q)_x =0

followed by a step with the ODE

   q_t = psi(q)

and src1.f90 generally solves the second equation in each grid cell, updating Q by dt * f(Q), for example, if Forward Euler is being used.

For more details you might see Chapter 17 of the book FVMHP or the slides fvmhp23_splitting.pdf for Lecture 23 that can be found in

  https://github.com/clawpack/fvmhp_materials/blob/main/slides_pdf/

The example David pointed to implements the geometric source term given in equation (18.54) of the book, for solving the radially symmetric acoustics equations.

There's also a simple example at

  https://www.clawpack.org/gallery/_static/apps/fvmbook/chap17/onramp/README.html

for a traffice flow example from the book.

 - Randy

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