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

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SUMMARY

The discussion focuses on solving two related non-linear equations using the Finite Volume Method (FVM) with a fully implicit scheme. The user faces challenges due to the presence of two unknowns in both equations, complicating the solution process. Participants suggest exploring numerical techniques specifically designed for coupled non-linear systems, emphasizing the importance of iterative solvers and proper discretization strategies. The conversation highlights the need for a robust approach to handle the interdependencies of the equations effectively.

PREREQUISITES
  • Understanding of Finite Volume Method (FVM)
  • Familiarity with fully implicit numerical schemes
  • Knowledge of non-linear equation solving techniques
  • Experience with iterative solvers for coupled systems
NEXT STEPS
  • Research iterative solvers such as Newton-Raphson for non-linear systems
  • Explore advanced discretization techniques in Finite Volume Method
  • Learn about convergence criteria for coupled non-linear equations
  • Investigate software tools like OpenFOAM for implementing FVM
USEFUL FOR

Mathematicians, computational engineers, and researchers working on numerical methods for solving non-linear equations, particularly those utilizing the Finite Volume Method.

zaynab
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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.

upload_2015-3-30_16-31-25.png


Any propositions?
Thank you.
 
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Sorry, i corrected the system:
upload_2015-3-30_17-42-19.png
 

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