l33 - Lecture 33: The SIMPLE Algorithm (Contd) 1 Last Time...

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1 Lecture 33: The SIMPLE Algorithm (Cont’d)
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2 Last Time … Looked into problem of introducing pressure into continuity equation for incompressible flows Introduced SIMPLE algorithm » Derived the pressure correction equation
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3 This Time … Look at the SIMPLE algorithm in detail Examine auxilliary issues » Under-relaxation and convergence Boundary conditions » Nature of pressure in incompressible flows
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4 SIMPLE Algorithm Semi-Implicit Method for Pressure-Linked Equations Proposed by Patankar and Spalding (1972) Idea is to start with discrete continuity equation Substitute into it the discrete u and v momentum equations » Discrete momentum equations contain pressure differences Hence get an equation for the discrete pressures » SIMPLE actually solves for a related quantity called the pressure correction
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5 SIMPLE Algorithm Solve momentum equations with guessed pressure field p* -- resulting velocity fields are u* and v* » Do not satisfy continuity because p* is wrong Propose corrections to velocities and pressure so that corrected velocities satisfy discrete continuity Let the corrected values be: Velocity corrections Pressure correction
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6 SIMPLE Algorithm (Cont’d) Also require that corrected velocities and pressures satisfy momentum equations: Subtracting starred momentum equations from above:   n n nb nb P N nb a v a v x p p  
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7 Velocity Correction Equation Make an approximation: Dropped '' and nb nb nb nb nb nb a u a v    n n P N a v x p p  
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8 Velocity Correction (Cont’d) Define: so that and   n n P N v d p p    * n n n P N v v d p p 
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l33 - Lecture 33: The SIMPLE Algorithm (Contd) 1 Last Time...

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