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| Keywords: Airflow-Obstructed-Duct.png N_S_Laminar svg A simulation using the navier-stokes differential equations of the aiflow into a duct at 0 003 m/s laminar flow The duct has a small obstruction in the centre that is parallel with the duct walls The observed spike is mainly due to numerical limitations This script which i originally wrote for scilab but ported to matlab porting is really really easy mainly convert comments -> // and change the fprintf and input statements Matlab was used to generate the image <pre> Matlab script to solve a laminar flow in a duct problem Constants inVel 0 003; Inlet Velocity m/s fluidVisc 1e-5; Fluid's Viscoisity Pa s fluidDen 1 3; Fluid's Density kg/m 3 MAX_RESID 1e-5; uhh residual units yeah deltaTime 1 5; seconds Kinematic Viscosity fluidKinVisc fluidVisc/fluidDen; Problem dimensions ductLen 5; m ductWidth 1; m grid resolution gridPerLen 50; m -1 gridDelta 1/gridPerLen; XVec 0 gridDelta ductLen-gridDelta; YVec 0 gridDelta ductWidth-gridDelta; Solution grid counts gridXSize ductLen gridPerLen; gridYSize ductWidth gridPerLen; Lay grid out with Y increasing down rows x decreasing down cols so subscripting becomes y x sorry velX zeros gridYSize gridXSize ; velY zeros gridYSize gridXSize ; newVelX zeros gridYSize gridXSize ; newVelY zeros gridYSize gridXSize ; Set initial condition for i 2 gridXSize-1 for j 2 gridYSize-1 velY j i 0; velX j i inVel; end end Set boundary condition on inlet for i 2 gridYSize-1 velX i 1 inVel; end disp velY 2 gridYSize-1 1 ; Arbitrarily set residual to prevent early loop termination resid 1+MAX_RESID; simTime 0; while deltaTime count 0; while resid > MAX_RESID count < 1e2 count count +1; for i 2 gridXSize-1 for j 2 gridYSize-1 newVelX j i velX j i + deltaTime fluidKinVisc / gridDelta 2 velX j i+1 + velX j+1 i - 4 velX j i + velX j-1 i + velX j i-1 - 1/ 2 gridDelta velX j i velX j i+1 - velX j i-1 + velY j i velX j+1 i - velX j i+1 ; newVelY j i velY j i + deltaTime fluidKinVisc / gridDelta 2 velY j i+1 + velY j+1 i - 4 velY j i + velY j-1 i + velY j i-1 - 1/ 2 gridDelta velY j i velY j i+1 - velY j i-1 + velY j i velY j+1 i - velY j i+1 ; end end Copy the data into the front for i 2 gridXSize - 1 for j 2 gridYSize-1 velX j i newVelX j i ; velY j i newVelY j i ; end end Set free boundary condition on inlet dv_x/dx dv_y/dx 0 for i 1 gridYSize velX i gridXSize velX i gridXSize-1 ; velY i gridXSize velY i gridXSize-1 ; end y velocity generating vent for i floor 2/6 gridXSize floor 4/6 gridXSize velX floor gridYSize/2 i 0; velY floor gridYSize/2 i-1 0; end calculate residual for conservation of mass resid 0; for i 2 gridXSize-1 for j 2 gridYSize-1 mass continuity equation using central difference approx to differential resid resid + velX j i+ 1 +velY j+1 i - velX j i-1 + velX j-1 i 2; end end resid resid/ 4 gridDelta 2 1/ gridXSize gridYSize ; fprintf 'Time 5 3f \t log10Resid 5 3f\n' simTime log10 resid ; simTime simTime + deltaTime; end mesh XVec YVec velX deltaTime input '\nnew delta time ' ; end Plot the results mesh XVec YVec velX </pre> en wikipedia 2007-02-24 User A1 wikipedia en User A1 original upload log page en wikipedia Airflow-Obstructed-Duct png 2007-02-24 05 45 User A1 1270×907×8 86796 bytes <nowiki>A simulation using the navier-stokes differential equations of the aiflow into a duct at 0 003 m/s laminar flow The duct has a small obstruction in the centre that is paralell with the duct walls The observed spike is mainly due to numerical limitatio</nowiki> Differential equations | ||||
