Ansys Icepak will solve the governing integral equations for mass and momentum, and (when appropriate) for energy and other scalars such as turbulence. A control-volume-based technique is used that consists of:
Division of the domain into discrete control volumes using a computational grid.
Integration of the governing equations on the individual control volumes to construct algebraic equations for the discrete dependent variables ("unknowns") such as velocities, pressure, temperature, and conserved scalars.
Linearization of the discretized equations and solution of the resultant linear equation system to yield updated values of the dependent variables.
The governing equations are solved sequentially (that is, segregated from one another). Because the governing equations are non-linear (and coupled), several iterations of the solution loop must be performed before a converged solution is obtained. Each iteration consists of the steps illustrated in Figure 40.7: Overview of the Solution Method and outlined below:
Fluid properties are updated, based on the current solution. (If the calculation has just begun, the fluid properties will be updated based on the initialized solution.)
The u, v and w momentum equations are each solved in turn using current values for pressure and face mass fluxes, in order to update the velocity field.
Because the velocities obtained in Step 2 may not satisfy the continuity equation locally, a "Poisson-type" equation for the pressure correction is derived from the continuity equation and the linearized momentum equations. This pressure correction equation is then solved to obtain the necessary corrections to the pressure and velocity fields and the face mass fluxes such that continuity is satisfied.
Where appropriate, equations for scalars such as turbulence, energy, and radiation are solved using the previously updated values of the other variables.
A check for convergence of the equation set is made.
These steps are continued until the convergence criteria are met.
Linearization
The discrete, non-linear governing equations are linearized to produce a system of equations for the dependent variables in every computational cell. The resultant linear system is then solved to yield an updated flow-field solution.
The manner in which the governing equations are linearized takes an "implicit" form with respect to the dependent variable (or set of variables) of interest. For a given variable, the unknown value in each cell is computed using a relation that includes both existing and unknown values from neighboring cells. Therefore each unknown will appear in more than one equation in the system, and these equations must be solved simultaneously to give the unknown quantities.
This will result in a system of linear equations with one equation for each cell in the domain. Because there is only one equation per cell, this is sometimes called a "scalar" system of equations. A point implicit (Gauss-Seidel) linear equation solver is used in conjunction with an algebraic multigrid (AMG) method to solve the resultant scalar system of equations for the dependent variable in each cell. For example, the x-momentum equation is linearized to produce a system of equations in which u velocity is the unknown. Simultaneous solution of this equation system (using the scalar AMG solver) yields an updated u-velocity field.
In summary, Ansys Icepak solves for a single variable field (for example, p) by considering all cells at the same time. It then solves for the next variable field by again considering all cells at the same time, and so on.