热流科学与工程西步文源大堂E教育部重点实验室neighboringnodes.The neglectofvelocity corrections oftheneighboringnodesattributes（归结于）thedrivingforceof utotallyto pressure correction,thus exaggerating（夸大)theaction of pressurecorrection6.4.3Numericalexample[Example 6-1(Text book))Known:Pw, Ps,ue, Vnuu.=0.7(pw-Pp)EV, = 0.6(ps - Pp)Ar=A=400Find: Pp,uw,V's中FD-NHT-EH6/41CENTER
6/41 6.4.3 Numerical example neighboring nodes. The neglect of velocity corrections of the neighboring nodes attributes ( 归结于) the driving force of ue ’ totally to pressure correction, thus exaggerating (夸 大) the action of pressure correction. [Example 6-1(Text book)] Known: , , , W S e n p p u v 0.7( ) w W P u p p 0.6( ) s S P v p p Find: , , P w s p u v 40 S p
热流科学与工程西步文源大堂E教育部重点实验室The key to solve Example 6-l:how to understand :uw=0.7(pw- Pp) v.=0.6(ps-Pp)They should be regarded as followsau =anbunb +b+ A(pp - pe)Eanun +b+PA(p-pe)=u +d.(pp-pe)aedFor thisu=0.7u,=0 + 0.7(pw- pp)exampled, =0.6Similarly,With this understanding , the problem can be solved accordingto the solution steps of SIMPLE algorithm. See Textbook中CFD-NHT-EHT7/41CENTER
7/41 The key to solve Example 6-1：how to understand : 0.7( ) w W P u p p They should be regarded as follows 0 0.7( ) w W P u p p 0.7 w d * * * * ( ) e e nb nb e P E a u a u b A p p * * * ( ) e e P E u d p p * * * * ( ) nb nb e e P E e e a u b A u p p a a For this example * 0 w u 0.6 ( ) s S P v p p Similarly， 0.6 s d With this understanding , the problem can be solved according to the solution steps of SIMPLE algorithm. See Textbook
热流科学与工程西步文源大学G教育部重点实验室6.5DiscussiononSIMPLEandConvergenceCriteriaofFlowFieldIteration6.5.1DiscussiononSIMPLEalgorithm1.Can the simplification approximations affect thecomputational results?2.Mathematically what type does the boundary conditionof thepressure correctionequation belong to?3.How to adopt the underrelaxation method in the flowfield iteration process?6.5.2ConvergencecriteriaofflowfielditerationCFD-NHT-EHTΦ8/41CENTER
8/41 6.5 Discussion on SIMPLE and Convergence Criteria of Flow Field Iteration 6.5.1 Discussion on SIMPLE algorithm 1.Can the simplification approximations affect the computational results? 2.Mathematically what type does the boundary condition of the pressure correction equation belong to ？ 3.How to adopt the underrelaxation method in the flow field iteration process？ 6.5.2 Convergence criteria of flow field iteration
热流科学与工程西步文源大堂E教育部重点实验室6.5DiscussiononSiMPLEandConvergenceCriteriaofFlowFieldIteration6.5.1DiscussiononSIMPLEalgorithm1.Can the two simplification approximations affect thecomputational results (solution accuracy) ?The approximations of SIMPLE will not affect theconverged solution, but do affect the convergence speedfor the following reasons:u°, v°, p* will be gradually(1)Theinconsistencybetweeneliminatedwiththeproceedingof iteration（随着迭代的进行）；(2) The term un, inu。 will gradually approach zero(趋近于O)withtheproceedingof iterationif itconverges!CFD-NHT-EHT中9/41CENTER
9/41 6.5 Discussion on SIMPLE and Convergence Criteria of Flow Field Iteration 6.5.1 Discussion on SIMPLE algorithm 1.Can the two simplification approximations affect the computational results (solution accuracy) ? The approximations of SIMPLE will not affect the converged solution , but do affect the convergence speed for the following reasons: 0 0 * (1) The inconsistency between u v p , , will be gradually eliminated with the proceeding of iteration（随着迭代的进行）； （2）The term in will gradually approach zero (趋近于0) with the proceeding of iteration if it converges! ' e u ' nb u
热流科学与工程西步文源大学E教育部重点实验室2. What type does the boundary condition of the pressurecorrection equation belong to ? Can it uniquely determine thesolution?(1)Mathematically the boundary condition of the pressurecorrection equation is Newmann condition,ap-Gresho's question (1991: A simple question to=0anSIMPLE users)(2) The adiabatic type boundary condition of the pressurecorrection equation can uniquely（唯一地）define anincompressible flow problem, becausepressure exists in theN-S equation in terms of gradient! This formulation can uniquelyU.u--lVp+Wdefine the flow fieldV.u=0 pThinking question: Why fortemperature not?No slip on the boundarySCFD-NHT-EI10/41CENTER
10/41 2. What type does the boundary condition of the pressure correction equation belong to ？Can it uniquely determine the solution? (1)Mathematically the boundary condition of the pressure correction equation is Newmann condition， ' 0 p n (2) The adiabatic type boundary condition of the pressure correction equation can uniquely (唯一地) define an incompressible flow problem, because pressure exists in the N-S equation in terms of gradient! 1 2 U U p U U 0 No slip on the boundary －Gresho’s question（1991：A simple question to SIMPLE users) This formulation can uniquely define the flow field. Thinking question: Why for temperature not?