l24 - Lecture 24 Flux Limiters 1 Last Time Developed a set...

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1 Lecture 24: Flux Limiters

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2 Last Time… Developed a set of limiter functions Second order accurate
3 This Time… Examine physical rationale for limiter functions Application to unstructured meshes

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4 Recall Higher-Order Scheme for e Consider finding face value using a second-order scheme with the gradient found at the upwind cell: Recall: What is the limiter function trying to do?   () 2 PW e P e x r x    EP e r
5 Limiter Functions =2r   0 for r 0 r

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6 Physical Interpretation The value of r can be thought of as the ratio of two gradients: Limiter chooses gradient adaptively to avoid creating extrema EP e PW r  Downwind cell gradient Upwind cell gradient ww
7 Case (a): Linear Variation Since: If variation is a straight line, on a uniform mesh, r=1 From our limiter function range, =1 for r=1 Can use either gradient and get the right value at e EP PW r  r=1

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l24 - Lecture 24 Flux Limiters 1 Last Time Developed a set...

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