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Introduction to Finite Volumes

Learn about finite volume approximation in numerical simulations. Explore balancing control volumes, adding source terms, and comparing different methods for solving equations. Discover how finite volumes relate to finite elements and finite differences in computational mathematics.

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Introduction to Finite Volumes

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  1. Introduction to Finite Volumes • R. Edwin García • redwing@purdue.edu

  2. average concentration: domain is partitioned into control volumes that fill the space Ω3 Ω2 Ω1 Ωi The Finite Volume Approximation

  3. i i i Ωi Balancing of Control Volume

  4. is the numerical flux i Balancing of a Control Volume

  5. i i Adding a Source Term

  6. Consider the Weak Solution: If you define: Both Approaches can be Shown to be Equivalent: 1 (subdomain collocation) flux entering/ leaving volume average value in volume = 0 Finite Volumes: A Special Case of Finite Elements

  7. Define: Finite Difference Methods

  8. Consider: Different Types of Finite Difference Schemes Forward Differences

  9. Different Types of Finite Difference Schemes Backward Differences Centered Differences

  10. Integrating the Solution Forward Euler: Backward Euler: Leap-Frog (or centered differences) Method:

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