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  "slug": "simple-algorithm",
  "title": "SIMPLE algorithm",
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  "lead": "In computational fluid dynamics (CFD), the SIMPLE algorithm is a widely used numerical procedure to solve the Navier–Stokes equations. SIMPLE is an acronym for Semi-Implicit Method for Pressure Linked Equations. The SIMPLE algorithm was developed by Prof. Brian Spalding and his student Suhas Patankar at Imperial College London in the early 1970s. Since then it has been extensively used by many researchers to solve different kinds of fluid flow and heat transfer problems. Many popular books on computational fluid dynamics discuss the SIMPLE algorithm in detail. A modified variant is the SIMPLER algorithm (SIMPLE Revised), that was introduced by Patankar in 1979.",
  "body": "In computational fluid dynamics (CFD), the SIMPLE algorithm is a widely used numerical procedure to solve the Navier–Stokes equations. SIMPLE is an acronym for Semi-Implicit Method for Pressure Linked Equations. The SIMPLE algorithm was developed by Prof. Brian Spalding and his student Suhas Patankar at Imperial College London in the early 1970s. Since then it has been extensively used by many researchers to solve different kinds of fluid flow and heat transfer problems. Many popular books on computational fluid dynamics discuss the SIMPLE algorithm in detail. A modified variant is the SIMPLER algorithm (SIMPLE Revised), that was introduced by Patankar in 1979. Update the pressure field: p^{k + 1} = p^k + \\text{urf} \\cdot p^{'} where urf is the under-relaxation factor for pressure. Update the boundary pressure corrections p_b^{'} . Correct the face mass fluxes: \\dot m_f^{k + 1} = \\dot m_f^{*} + \\dot m_f^{'} Correct the cell velocities: \\vec v^{k + 1} = \\vec v^{*} - \\frac ; where {\\nabla p^{'} } is the gradient of the pressure corrections, {\\vec a_P^v } is the vector of central coefficients for the discretized linear system representing the velocity equation and Vol is the cell volume. Update density due to pressure changes. ==References==",
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    "title": "SIMPLE algorithm",
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