l32 - Lecture 32: The SIMPLE Algorithm 1 Last Time Looked...

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1 Lecture 32: The SIMPLE Algorithm
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2 Last Time … Looked at where to store pressure vis-à-vis velocity » Checkerboarding problems Looked at staggered mesh as a remedy for checker- boarding for structured meshes
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3 This Time … Look into problem of introducing pressure into continuity equation for incompressible flows Introduce SIMPLE algorithm
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4 Remedy: Staggered Mesh Store pressure at main cell centroids Store velocities on staggered control volumes
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5 Staggered Mesh: Momentum Equations Pressure difference for u e Pressure difference for v n No need to interpolate pressure to face » Available on faces of momentum cv’s Pressure checkerboarding avoided x
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6 Staggered Mesh: Continuity Equation Discretize continuity equation on main control volume: No need to interpolate velocities – no checkerboarding Velocities available on face where needed
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7 Discrete Equations Continuity: U-momentum: V-Momentum:
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8 Momentum Equation Neighbors Neighbors of u e are shown Neighbors of v n ?
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9 Motivation Can use either sequential or direct methods Sequential methods solve continuity and momentum equations sequentially: » Discretize continuity over domain » Solve continuity » Discretize u-momentum eqn over domain » Solve for u velocity » Discretize v-momentum eqn over domain » Solve for v velocity » Repeat until convergence
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10 Motivation (Cont’d) Direct methods: » Discretize all governing equations over domain » Create large linear system » x is a vector of 4N unknowns in 3D (3 velocities, one pressure, N cells) Direct methods too expensive even today Ax = b
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11 Pressure-Based Methods
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l32 - Lecture 32: The SIMPLE Algorithm 1 Last Time Looked...

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