CFD Online Discussion Forums - SIMPLER Algorithm

Hello.

I have some questions about the implementation of the SIMPLER algorithm outlined in Patankar's book, Numerical Heat Transfer and Fluid Flow.

I am implementing a one dimensional version with a uniform grid.

||-o-|-o-|-o-||

o shows where the pressure is calculated, | the velocity and || represents the given boundary velocities.

1) Do I use TDMA to calculate the pseudo velocities (u^)? Or do I just iterate through the array, calculating the coefficients (ap, aw, ae, b) and the pseudo velocity as I go?

2) When calculating the pressure field from the pseudo velocity values,the coefficients aE and aW include ae and aw.

aE = density * (Area / ae) *Dy *Dz

But since the grid is staggered ae does not exist at the point P, where the pressure is calculated. Am I meant to use ap from the point ue (the neighbouring velocity)?

3) In the grid setup shown, there is no boundary pressure value. When I start the TDMA process for pressure, there is no aW coefficient (ie c1 = 0 in the TDMA notation used in the book) and P1 is consequently equal to 1. This means that all subsequent values of Pi are also 1. Is this correct? It doesn't seem like it can be as on the far boundary aE does not exist and QN involves a division by zero.

4) Since I am assuming an incompressible fluid, the density never changes and so terms like (d0 - d) become zero. Is this correct?

Thankyou to anyone who can help me with this.