l36 - Lecture 36 Co-Located Schemes 1 Last Time Completed...

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1 Lecture 36: Co-Located Schemes
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2 Last Time … Completed looking at SIMPLE on staggered structured Cartesian meshes Found that staggered meshes are difficult to use on body-fitted meshes and unstructured meshes
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3 This Time… Start looking at co-located pressure-velocity storage Consider what needs to be done to prevent checkerboarding » Get around linear interpolation of pressure Figure out discretization accuracy
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4 Recall… Storing pressure and velocity at cell centroids leads to checker-boarding Comes from having to interpolate pressure to the face and finding p for the cell; similar problem with velocity in continuity equation Remedy is a staggered mesh » Increased geometric complexity even on structured meshes » Nearly impossible for unstructured meshes
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5 Co-Located Storage Store (u,v,P, ) at cell centroid Same control volume for all Also sometimes called equal-order interpolation or a non- staggered formulation
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6 Discrete Momentum Equation Let‟s do this in 1D to avoid algebra; assume uniform mesh Discrete momentum equation for velocity u p : We are writing an equation for u P but we need u e
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7 Momentum Equation (Cont’d) Interpolating pressure linearly, we get:
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8 Pressure Checker-Boarding Divide momentum equations by center coefficients: Here:
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This note was uploaded on 12/29/2011 for the course ME 608 taught by Professor Na during the Fall '10 term at Purdue.

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l36 - Lecture 36 Co-Located Schemes 1 Last Time Completed...

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