Solving the Fluid Pressure Poisson Equation Using Multigrid-Evaluation and Improvements.

Area of Science:

• Computational fluid dynamics
• Numerical analysis
• Scientific computing

Background:

• Incompressible Navier-Stokes equations require solving the pressure Poisson equation for mass conservation in fluid simulations.
• Standard multigrid solvers face convergence challenges in complex domains and lack adaptability to different discretizations.
• Existing methods are often specific to particular numerical schemes, limiting their broad applicability.

Purpose of the Study:

• To analyze multigrid solver convergence for the pressure Poisson equation in diverse simulation domains.
• To develop a generic multigrid solver that improves convergence rates and adapts to various discretizations.
• To evaluate the performance of the proposed solver with finite difference and finite volume methods.

Main Methods:

• Analysis of multigrid solver convergence properties for the pressure Poisson equation.
• Development of a graph-based extension to define coarse grid hierarchies.
• Implementation and evaluation of the generic multigrid solver with finite difference and finite volume discretizations.

Main Results:

• The proposed graph-based multigrid solver demonstrates improved convergence rates in complex simulation domains.
• The solver is generic and applicable to different discretizations of the pressure Poisson equation.
• Multigrid schemes can achieve high performance even in complicated scenarios, with a trade-off in memory consumption.

Conclusions:

• A novel, generic multigrid solver enhances pressure Poisson equation solving in fluid dynamics simulations.
• The graph-based coarse grid hierarchy approach overcomes limitations of existing solvers.
• The method offers improved efficiency for complex simulations, albeit with higher memory requirements.