### 1.4.3. Solving the CFD Problem

The component that solves the CFD problem is called the Solver. It produces the required results in a non-interactive/batch process. A CFD problem is solved as follows:

1. The partial differential equations are integrated over all the control volumes in the region of interest. This is equivalent to applying a basic conservation law (for example, for mass or momentum) to each control volume.

2. These integral equations are converted to a system of algebraic equations by generating a set of approximations for the terms in the integral equations.

3. The algebraic equations are solved iteratively.

An iterative approach is required because of the nonlinear nature of the equations, and as the solution approaches the exact solution, it is said to converge. For each iteration, an error, or residual, is reported as a measure of the overall conservation of the flow properties.

How close the final solution is to the exact solution depends on a number of factors, including the size and shape of the control volumes and the size of the final residuals. Complex physical processes, such as combustion and turbulence, are often modeled using empirical relationships. The approximations inherent in these models also contribute to differences between the CFD solution and the real flow.

The solution process requires no user interaction and is, therefore, usually carried out as a batch process.

The solver produces a results file that is then passed to the post-processor.

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