Numerical Heat Transfer（数值传热学）Chapter6PrimitiveVariableMethodsforEllipticFlowandHeatTransfer (2)1/43
1/43 Numerical Heat Transfer (数值传热学) Chapter 6 Primitive Variable Methods for Elliptic Flow and Heat Transfer（2）
6.1Source terms in momentumeguationsand two keyissuesinnumericallysolvingmomentumeguation6.2 Staggered grid system and discretization ofmomentumeguation6.3PressurecorrectionmethodsforN-Sequation6.4ApproximationsinSIMPLEalgorithm6.5DiscussiononSIMPLEalgorithmandcriteriaforconvergence6.6DevelopmentsofSIMPLEalgorithm6.7Boundaryconditiontreatmentsforopensystem6.8Fluidflow&heat transferinaclosed system2/43
2/43 6.1 Source terms in momentum equations and two key issues in numerically solving momentum equation 6.2 Staggered grid system and discretization of momentum equation 6.3 Pressure correction methods for N-S equation 6.4 Approximations in SIMPLE algorithm 6.5 Discussion on SIMPLE algorithm and criteria for convergence 6.6 Developments of SIMPLE algorithm 6.7 Boundary condition treatments for open system 6.8 Fluid flow & heat transfer in a closed system
6.4ApproximationsmadeinSIMPLEalgorithm6.4.1CalculationprocedureofSIMPLEalgorithm6.4.2ApproximationsinSIMPLEalgorithm1.Inconsistenacy（不一致性）of initialfieldassumptions2.Overestimating（夸大）theeffects of pressurecorrectionofneighboringnodes6.4.3Numericalexample3/43
3/43 6.4.1 Calculation procedure of SIMPLE algorithm 6.4.2 Approximations in SIMPLE algorithm 6.4.3 Numerical example 1.Inconsistenacy (不一致性) of initial field assumptions 2.Overestimating (夸大) the effects of pressure correction of neighboring nodes 6.4 Approximations made in SIMPLE algorithm
6.4ApproximationsinSIMPLEAlgorithm6.4.1CalculationprocedureofSIMPLEalgorithm1. Assuming initial velocity fields, u 0 and y o, to determinethe coefficients of the discretized momentum equations;2. Assuming an initial pressure field, p *;3. Solving the discretized momentum equation based on p *obtaining u *,v *;4. Solving pressure correction equation, obtaining p ';5. Revising pressure and velocities by p ': p =p *+α,pu=u+u=u+dApV=V,+V,=V,+d,Ap4/43
4/43 6.4 Approximations in SIMPLE Algorithm 6.4.1 Calculation procedure of SIMPLE algorithm 1. Assuming initial velocity fields, u 0 and v 0 , to determine the coefficients of the discretized momentum equations； 2. Assuming an initial pressure field, p *； 3. Solving the discretized momentum equation based on p * , obtaining u *,v *; 4. Solving pressure correction equation, obtaining p ’； 5. Revising pressure and velocities by p ’ ：p = p *+ p ’ p * ' * ' e e e e e u u u u d p = + = + * ' * ' n n n n n v v v v d p = + = +
6a. Solving other scalar variables coupled with velocity ;6b. Starting next iteration with u = u。 + ue, v = v, + y,and p= p' + α,p as the solutions of the flow fieldat present iteration level.In the following discussion focus will be paid on the solutionof flow field, and Step 6a will be ignored（忽略）.The entiresolution procedure is composed of six steps.SIMPLE=Semi-implicit method for pressure-linkedequations(求解压力耦合问题的半隐方法)where “semi-implicit" refers to the neglect of the velocitycorrection effects of the neighboring grids5/43
5/43 6a. Solving other scalar variables coupled with velocity； In the following discussion focus will be paid on the solution of flow field, and Step 6a will be ignored （忽略）. The entire solution procedure is composed of six steps. 6b. Starting next iteration with and as the solutions of the flow field at present iteration level. * ' e e u u u = + ， * ' p p p p = + * ' n n v v v = + SIMPLE=Semi-implicit method for pressure-linked equations(求解压力耦合问题的半隐方法)- where “semi-implicit” refers to the neglect of the velocity correction effects of the neighboring grids