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Introduction to Finite Volumes

Introduction to Finite Volumes. R. Edwin García redwing@purdue.edu. average concentration:. domain is partitioned into control volumes that fill the space. Ω 3. Ω 2. Ω 1. Ω i. The Finite Volume Approximation. i. i. i. Ω i. Balancing of Control Volume. is the numerical flux. i.

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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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