# l37 - Lecture 37 Co-Located Schemes(continued 1 Last Time...

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1 Lecture 37: Co-Located Schemes (continued)

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2 Last Time … Started looking at co-located pressure-velocity storage Developed momentum-interpolation scheme Figured out discretization accuracy
3 This Time… Complete development of co-located scheme Start looking at SIMPLE algorithm for co-located scheme

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4 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
5 Momentum Equation (Cont’d) Interpolating pressure linearly, we get:

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6 Variable Definitions Divide momentum equations by center coefficients: Here:
7 Co-Located Formulation Velocity interpolation to the face: We are subtracting the ‘alternate’ pressure term and adding in an ‘adjacent’ pressure term

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8 Equivalent Model Equation Starting with We obtain the model equation: Added dissipation term
9 Accuracy of Added Dissipation Scheme Recall momentum interpolation formula: Let’s look at accuracy of first term. Expanding velocities in Taylor series

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10 Accuracy (Cont’d) Accuracy of first term: We showed the second term to be: Third-order term
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l37 - Lecture 37 Co-Located Schemes(continued 1 Last Time...

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