Pressure boundary conditions for immersed-boundary methods.

Area of Science:

• Computational Fluid Dynamics
• Numerical Analysis

Background:

• Immersed boundary methods are increasingly popular for simulating fluid flows with complex, moving, or deforming boundaries.
• Traditional fractional-step methods often struggle with enforcing boundary conditions on immersed bodies, leading to errors in pressure and coupled domain solutions.
• Existing methods that enforce both velocity and pressure boundary conditions typically require complex, iterative solvers.

Purpose of the Study:

• To develop a new formulation for immersed boundary methods that efficiently enforces boundary conditions on pseudo-pressure within fractional-step approaches.
• To overcome limitations of existing methods, such as slip-errors and the need for complex solvers.

Main Methods:

• A novel fractional-step formulation inspired by the ghost-fluid method is proposed.
• Boundary condition enforcement for pseudo-pressure is integrated into the right-hand side of a standard Poisson equation.
• The approach allows for the utilization of fast solvers, such as those based on trigonometric transformations.

Main Results:

• The proposed method successfully incorporates necessary modifications for boundary condition enforcement directly into the Poisson equation's right-hand side.
• This enables the use of efficient, standard Poisson solvers, avoiding computationally expensive iterative methods.
• The formulation demonstrates accuracy and robustness across a range of increasingly complex test cases.

Conclusions:

• The new formulation provides an efficient and accurate way to handle pressure boundary conditions in immersed boundary fractional-step methods.
• It simplifies the computational process by allowing the use of standard, fast Poisson solvers.
• This advancement has significant implications for the simulation of fluid dynamics problems with complex geometries and moving boundaries.