热流科学与工程西步文源大学E教育部重点实验室Numerical HeatTransfer（数值传热学）Chapter6PrimitiveVariableMethodsforEllipticFlowandHeatTransfer(2)raInstructorTao,Wen-QuanKeyLaboratoryofThermo-FluidScience&EngineeringInt.JointResearchLaboratoryofThermalScience&EngineeringXi'anJiaotongUniversityInnovativeHarborofWestChina,Xian2022-October-25CFD-NHT-EHTΦ1/41CENTER
1/41 Instructor Tao, Wen-Quan Key Laboratory of Thermo-Fluid Science & Engineering Int. Joint Research Laboratory of Thermal Science & Engineering Xi’an Jiaotong University Innovative Harbor of West China, Xian 2022-October-25 Numerical Heat Transfer (数值传热学) Chapter 6 Primitive Variable Methods for Elliptic Flow and Heat Transfer（2）
热流科学与工程西步文通大堂E教育部重点实验室6.4ApproximationsinSIMPLEalgorithm6.4.1CalculationprocedureofSiMPLEalgorithm6.4.2ApproximationsinSIMPLEalgorithm1.Inconsistenacy（不一致性）ofinitialfieldassumptions2.Overestimating（夸大）theeffectsofpressurecorrection of neighboring nodes6.4.3NumericalexampleΦCFD-NHT-EHT2/41CENTER
2/41 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 in SIMPLE algorithm
热流科学与工程西步文源大堂E教育部重点实验室6.4ApproximationsinSIMPLEAlgorithm6.4.1CalculationprocedureofSIMPLEalgorithm1. Assuming initial velocity fields, u o and v 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 *,y *;4. Solving pressure correction equation, obtaining p ';5. Revising pressure and velocities by p ': p =p *+α,pV=V,+V,=V,+d,Ap,u=u。+u=u.+dApCFD-NHT-EHTΦ3/41CENTER
3/41 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
热流科学与工程西步文源大学G教育部重点实验空6a. Solving other scalar variables coupled with velocity ;6b. Starting next iteration with u = u。 + ue, v = v, + v,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. The entire solutionprocedure is composed of six stepsSIMPLE=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 velocity correctioneffects of the neighboring grids.ΦCFD-NHT-EHT4/41CENTER
4/41 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. 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 velocity correction effects of the neighboring grids
热流科学与工程西步文源大学E教育部重点实验室6.4.2ApproximationsinSIMPLEalgorithmSIMPLE is the dominant algorithm for solvingincompressible flows. It was proposed in 1972. Since thenmany variants (方案)were proposed to improve (overcome)following two assumptions.1.Inconsistency（不一致性）ofinitialfieldassumptionsIn SIMPLEu,andp* are assumed independentlyActuallythereissomeinherent（固有的）relationshipbetweenvelocityandpressure,2.Overestimating（大)theeffectsofpressurecorrectionof the neighboring nodes. Because ue 'is caused by boththe pressure correction and velocity corrections of itsCFD-NHT-EHTΦ5/41CENTER
5/41 6.4.2 Approximations in SIMPLE algorithm SIMPLE is the dominant algorithm for solving incompressible flows. It was proposed in 1972. Since then many variants (方案) were proposed to improve (overcome) following two assumptions. 1.Inconsistency (不一致性) of initial field assumptions In SIMPLE u 0 ,v 0 and p * are assumed independently. Actually there is some inherent (固有的）relationship between velocity and pressure; 2.Overestimating (夸大)the effects of pressure correction of the neighboring nodes. Because ue ’ is caused by both the pressure correction and velocity corrections of its