How can I solve two related non-linear equations using EDP finite volume method?

Thread starter zaynab
Start date Mar 30, 2015
Tags

Finite Volume

In summary, EDP finite volume solving is a numerical method used to solve partial differential equations (EDPs) by dividing the domain into smaller control volumes and discretizing the equations to solve for the unknown variables at each control volume. It differs from other numerical methods by focusing on fluxes at control volume boundaries and has advantages such as handling complex geometries, ensuring conservation, and being easily parallelized. However, it may not be suitable for problems with steep gradients or discontinuities and requires careful treatment of boundary conditions. In practice, it involves breaking down the problem into control volumes, discretizing the equations, and using iterative techniques to solve the resulting system of equations with specialized software packages or programming languages.

Mar 30, 2015

zaynab

Hi evryone,
the system i am working on, is composed of two relatied non-linear equations that I discretised using finite volume method with fully implicit scheme, the difficulty is that the two unknonw appear in both equations and i don't know how to solve it.

Any propositions?
Thank you.

Physics news on Phys.org

Mar 30, 2015

zaynab

Sorry, i corrected the system:

1. What is EDP finite volume solving?

EDP finite volume solving is a numerical method used to solve partial differential equations (EDPs). It involves dividing the domain into smaller control volumes and discretizing the equations to solve for the unknown variables at each control volume. This method is commonly used in computational fluid dynamics and other scientific fields.

2. How does EDP finite volume solving differ from other numerical methods?

Unlike other numerical methods such as finite difference or finite element methods, EDP finite volume solving focuses on the fluxes or flow rates at the boundaries of each control volume rather than the values at each individual point. This makes it well-suited for problems involving conservation laws.

3. What are the advantages of using EDP finite volume solving?

One of the main advantages of EDP finite volume solving is its ability to handle complex geometries and boundary conditions. It also ensures conservation of mass, energy, and other quantities, making it a reliable method for solving physical problems. Additionally, it can be easily parallelized for faster computation.

4. Are there any limitations to EDP finite volume solving?

EDP finite volume solving may not be suitable for problems with steep gradients or discontinuities in the solution. It also requires careful treatment of boundary conditions, and the accuracy of the solution may be affected by the choice of control volumes and discretization schemes.

5. How is EDP finite volume solving implemented in practice?

In practice, EDP finite volume solving involves breaking down the problem into smaller control volumes, discretizing the equations using a numerical method such as the finite volume method, and solving the resulting system of equations using iterative techniques. Specialized software packages and programming languages such as MATLAB and Python are often used for implementation.