1 / 11

Lecture 12: Control-Volume Approach (time-variable)

Lecture 12: Control-Volume Approach (time-variable). CE 498/698 and ERS 685 Principles of Water Quality Modeling. t. i, l +1. l + 1. D t. i -1 , l. i, l. i +1, l. l. D x. i, l -1. l - 1. forward difference over time. x. i. i- 1. i+ 1. finite difference approximations. t.

efuru
Download Presentation

Lecture 12: Control-Volume Approach (time-variable)

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Lecture 12: Control-Volume Approach (time-variable) CE 498/698 and ERS 685 Principles of Water Quality Modeling Lecture 12

  2. t i,l+1 l+1 Dt i-1,l i,l i+1,l l Dx i,l-1 l-1 forward difference over time x i i-1 i+1 finite difference approximations Lecture 12

  3. t i,l+1 l+1 Dt i-1,l i,l i+1,l l Dx i,l-1 l-1 x i i-1 i+1 centered difference over space finite difference approximations Lecture 12

  4. t i,l+1 l+1 Dt i-1,l i,l i+1,l l Dx i,l-1 l-1 x i i-1 i+1 centered difference over space finite difference approximations Lecture 12

  5. t i,l+1 l+1 Dt i-1,l i,l i+1,l l Dx i,l-1 l-1 x i i-1 i+1 finite difference approximations backward difference over space Lecture 12

  6. forward difference over time centered difference over space centered difference over space finite difference approximations FTCS Lecture 12

  7. l+1 l i-1 i i+1 second derivative with space first derivative with time FTCS explicit method Lecture 12

  8. must be positive! Control-Volume Approach Lecture 12

  9. Assuming Q, E, V, k are constant: What if we used backward difference for space derivative? or Courant condition: Solution stability If we have purely advective system: Lecture 12

  10. where and and centered diff: forward diff: backward diff: Weighted Differences Lecture 12

  11. Stability criterion: spatial temporal Solution stability Numerical dispersion: Lecture 12

More Related