The pressure-based solver employs an algorithm which belongs to a general class of methods called the projection method [ 58]. In the projection method, wherein the constraint of mass conservation (continuity) of the velocity field is achieved by solving a pressure (or pressure correction) equation. The pressure equation is derived from the continuity and the momentum equations in such a way that the velocity field, corrected by the pressure, satisfies the continuity. Since the governing equations are nonlinear and coupled to one another , the solution process involves iterations wherein the entire set of governing equations is solved repeatedly until the solution converges.
Two pressure-based solver algorithms are available in FLUENT. A segregated algorithm, and a coupled algorithm. These two approaches are discussed in the sections below.
The Pressure-Based Segregated Algorithm
The pressure-based solver uses a solution algorithm where the governing equations are solved sequentially (i.e., segregated from one another). Because the governing equations are non-linear and coupled, the solution loop must be carried out iteratively in order to obtain a converged numerical solution.
In the segregated algorithm, the individual governing equations for the solution variables (e.g., , , , , , , , etc.) are solved one after another . Each governing equation, while being solved, is "decoupled" or "segregated" from other equations, hence its name. The segregated algorithm is memory-efficient, since the discretized equations need only be stored in the memory one at a time. However, the solution convergence is relatively slow, inasmuch as the equations are solved in a decoupled manner.
With the segregated algorithm, each iteration consists of the steps illustrated in Figure 25.1.1 and outlined below:
These steps are continued until the convergence criteria are met.
The Pressure-Based Coupled Algorithm
Unlike the segregated algorithm described above, the pressure-based coupled algorithm solves a coupled system of equations comprising the momentum equations and the pressure-based continuity equation. Thus, in the coupled algorithm, Steps 2 and 3 in the segregated solution algorithm are replaced by a single step in which the coupled system of equations are solved. The remaining equations are solved in a decoupled fashion as in the segregated algorithm.
Since the momentum and continuity equations are solved in a closely coupled manner, the rate of solution convergence significantly improves when compared to the segregated algorithm. However, the memory requirement increases by 1.5 - 2 times that of the segregated algorithm since the discrete system of all momentum and pressure-based continuity equations needs to be stored in the memory when solving for the velocity and pressure fields (rather than just a single equation, as is the case with the segregated algorithm).