# SIMPLE algorithm for solving blasius flow

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 December 10, 2011, 14:46 SIMPLE algorithm for solving blasius flow #1 New Member   Join Date: Dec 2011 Posts: 5 Rep Power: 6 i've tried solving 2 dimensional N-S equations for blasius flow bt wd sum absurd results. i 2k d equations from d book on cfd by j.d anderson. i m facing difficulty with how to give the boundary conditions,nebody plz help me. d prob is dat,d code runs well bt d reuslts r far away from reality m using SIMPLE algorithm with staggered grid................. plzzzzzzzzzzzzz help me ............. thnx

 December 18, 2011, 01:22 #2 New Member   Mazhar Iqbal Join Date: Mar 2009 Posts: 10 Rep Power: 9 There are few typo mistakes in Anderson book. If you can share your code perhaps I can help you. My Email ID is iqbalmazhar107@yahoo.com tanmoy likes this.

 December 22, 2011, 05:44 #3 New Member   Join Date: Dec 2011 Posts: 5 Rep Power: 6 hey,dis is my code. i've written it in C. plz help me............. #include #include #include void main() { /* declaration of variables*/ float U,rho,meu,L,Re,udt,uddt,vdt,vddt,a1,a2,a3,a4,b1,b2 ,b3,b4,P; float dt,dx,A,B,dy,u[11][22],v[12][23],p[11][21],pdash[11][21],a,b,c,d; int pr,pc,ur,uc,vr,vc,k; //counters FILE *f=fopen("output1.txt","w"); FILE *g=fopen("output2.txt","w"); FILE *s=fopen("output3.txt","w"); clrscr(); printf ("\nEnter the free stream velocity: "); scanf ("%f",&U); printf ("\nEnter the length of the plate: "); scanf ("%f",&L); printf ("\nEnter the pressure at the inlet:"); scanf ("%f",&P); printf ("\nEnter the value of density of the fluid: "); scanf ("%f",&rho); printf ("\nEnter the value of coefficient of viscosity: "); scanf ("%f",&meu); Re=(rho*U*L)/meu; printf ("\nThe reynold's number is: %f",Re); //initializing the matrices for (ur=0;ur<=10;ur++) { for (uc=0;uc<=21;uc++) { u[ur][uc]=0; } } for (vr=0;vr<=11;vr++) { for (vc=0;vc<=22;vc++) { v[vr][vc]=0; } } for (pr=0;pr<=10;pr++) { for (pc=0;pc<=20;pc++) { p[pr][pc]=0; pdash[pr][pc]=0; } } //giving the velocity spike v[2][4]=(U)/2; dx=L/20; dy=0.001378; dt=.001; for (k=0;k<=250;k++) { for (uc=0;uc<=21;uc++) { u[10][uc]=U; u[0][uc]=0; } for (vc=0;vc<=22;vc++) { v[0][vc]=-v[1][vc]; v[11][vc]=-v[10][vc]; } for (ur=0;ur<=10;ur++) { u[ur][0]=2*U-u[ur][1]; } for (vr=0;vr<=11;vr++) { v[vr][1]=0; v[vr][0]=0; } for (pr=0;pr<=10;pr++) { pdash[pr][0]=0; pdash[pr][20]=0; } for (pc=0;pc<=20;pc++) { pdash[0][pc]=0; pdash[10][pc]=0; } //calculating the u-velocity at all the internal nodes for (ur=1,pr=1,vr=1;ur<=9;ur++,pr++,vr++) { for (uc=1,pc=1,vc=1;uc<=20;uc++,pc++,vc++) { vdt=(v[vr+1][vc]+v[vr+1][vc+1])/2; vddt=(v[vr][vc]+v[vr][vc+1])/2; a1=(rho*(u[ur][uc+1]*u[ur][uc+1]-u[ur][uc-1]*u[ur][uc-1]))/(2*dx); a2=(rho*(u[ur+1][uc]*vdt-u[ur-1][uc]*vddt))/(2*dy); a3=(u[ur][uc+1]-2*u[ur][uc]+u[ur][uc-1])/(dx*dx); a4=(u[ur+1][uc]-2*u[ur][uc]+u[ur-1][uc])/(dy*dy); A=-(a1+a2)+meu*(a3+a4); u[ur][uc]=u[ur][uc]+((A*dt)/rho)-(dt/(rho*dx))*(p[pr][pc]-p[pr][pc-1]); } } //calculating the v-velocity at all the internal nodes for (vr=2,ur=1,pr=1;vr<=11;vr++,ur++,pr++) { for (vc=2,uc=1,pc=1;vc<=21;vc++,uc++,pc++) { udt=(u[ur-1][uc+1]+u[ur][uc+1])/2; uddt=(u[ur-1][uc]+u[ur][uc])/2; b1=(rho*(v[vr-1][vc+1]*udt-v[vr-1][vc-1]*uddt))/(2*dx); b2=(rho*(v[vr][vc]*v[vr][vc]-v[vr-2][vc]*v[vr-2][vc]))/(2*dy); b3=(v[vr-1][vc+1]-2*v[vr-1][vc]+v[vr-1][vc-1])/(dx*dx); b4=(v[vr][vc]-2*v[vr-1][vc]+v[vr-2][vc])/(dy*dy); B=-(b1+b2)+meu*(b3+b4); v[vr-1][vc]=v[vr-1][vc]+((B*dt)/rho)-(dt/(rho*dx))*(p[pr][pc]-p[pr-1][pc]); } } for (ur=0;ur<=10;ur++) { u[ur][21]=u[ur][20]; } for (vr=0;vr<=22;vr++) { v[vr][22]=v[vr][21]; } for (pr=1,ur=1,vr=2;pr<=9;pr++,ur++,vr++) { for (pc=1,uc=1,vc=2;pc<=19;pc++,uc++,vc++) { a=2*((dt)/(dx*dx)+(dt)/(dy*dy)); b=-(dt/(dx*dx)); c=-(dt/(dy*dy)); d=(1/dx)*(rho*(u[ur][uc+1]-u[ur][uc]))+(1/dy)*(rho*(v[vr][vc]-v[vr-1][vc])); pdash[pr][pc]=-(1/a)*(b*(pdash[pr][pc+1]+pdash[pr][pc-1])+c*(pdash[pr+1][pc]+pdash[pr-1][pc])+d); } } for (pr=0;pr<=10;pr++) { for (pc=0;pc<=20;pc++) { p[pr][pc]=p[pr][pc]+0.1*pdash[pr][pc]; } } } for (ur=0;ur<=10;ur++) { for (uc=0;uc<=21;uc++) { printf("\nu[%d][%d]=%f",ur,uc,u[ur][uc]); fprintf(f,"\nu[%d][%d]=%f",ur,uc,u[ur][uc]); } } getch(); }

 January 1, 2012, 12:07 #4 New Member   Mazhar Iqbal Join Date: Mar 2009 Posts: 10 Rep Power: 9 Sorry for the delay, but I am not familiar with C++. I have written a program for Couttee flow, as discussed by Anderson, in MATLAB. If you are interested I can post it here.

 January 3, 2012, 11:53 #5 New Member   Vishnu Prasad Join Date: Sep 2010 Location: Goa Posts: 19 Rep Power: 8 If you are trying to solve the flat plate problem numerically, its a waste of time to try and solve the NS. Solve the simplified and final equation, which is the blasius equation for a flat plate. Its one dimentional( on eta) though non-linear, can be solved easily by runge kutta( any order ) shooting method or traditional (non-linear) difference method. I would recommend Applied Numerical Analysis by Brian Bradie. The treatment of theory of convergence and order is good and the style of explanation excellent. There is a slight problem in implementing shooting method, since the initial condition of f(0) is unknown.But a predictor corrector would do the trick. tanmoy likes this.

 January 9, 2012, 12:19 #6 New Member   Join Date: Dec 2011 Posts: 5 Rep Power: 6 dear mazhar,plz do it na...... wl be greatful to u for ur help.ty

 Tags blasius flow, navier stokes equations, simple algorithm

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