Question

The equation for pressure of the SIMPLER algorithm is obtained using _________

(a) continuity equation in the PDE form

(b) discretized continuity equation

(c) momentum equation in the PDE form

(d) discretized momentum equation

I have been asked this question during an interview.

My doubt is from Incompressible Flows topic in portion Incompressible Flows & Compressible Flows of Computational Fluid Dynamics

Answer 1

The SIMPLER (Semi-Implicit Method for Pressure-Linked Equations Revised) algorithm is used to solve incompressible flow problems in Computational Fluid Dynamics (CFD). The pressure correction equation in the SIMPLER method is derived using a discretized form of the continuity equation, which ensures that mass conservation is satisfied during the solution process.

Here’s a breakdown of the options:

• (a) Continuity equation in the PDE form: The continuity equation in its partial differential equation (PDE) form is used to express the mass conservation, but the SIMPLER algorithm specifically uses the discretized form for pressure correction.

• (b) Discretized continuity equation: Correct. In the SIMPLER algorithm, the pressure correction equation is derived from the discretized form of the continuity equation. This discretization helps to ensure that the mass conservation constraint is satisfied in the computational domain.

• (c) Momentum equation in the PDE form: The momentum equation is essential for velocity calculations but does not directly provide the pressure correction equation in SIMPLER.

• (d) Discretized momentum equation: While the momentum equation is important for calculating velocity fields, it is not used to directly derive the pressure correction equation in SIMPLER.

Correct Answer: (b) Discretized continuity equation