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Advection and Diffusion Equations

In: Computational Methods in Engineering

Author

Listed:
  • S. P. Venkateshan

    (Indian Institute of Technology Madras, Department of Mechanical Engineering)

  • Prasanna Swaminathan

    (Universite Sorbonne Paris Nord, Charge de recherche 2)

Abstract

A PDE with time as one of its independent variable is an initial value problem. The right-hand side of the above equations is function of space variables alone. The terms involving spatial derivatives can be discretized using FDM, collocation, FEM, FVM and other suitable methods. Let us consider the diffusion equation whose spatial derivative is discretized using second order central difference. Then we have a set of ODEs with time as the independent variable and the function values at the nodes as the dependent variable.

Suggested Citation

  • S. P. Venkateshan & Prasanna Swaminathan, 2023. "Advection and Diffusion Equations," Springer Books, in: Computational Methods in Engineering, chapter 0, pages 651-707, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-08226-9_14
    DOI: 10.1007/978-3-031-08226-9_14
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