Force-amplified, single-sided diffused-interface immersed boundary kernel for correct local velocity gradient...

Area of Science:

• Computational fluid dynamics
• Numerical methods for fluid flow

Background:

• Current diffused-interface immersed boundary methods (IBM) inaccurately compute velocity gradients at solid-fluid interfaces due to force distribution affecting Navier-Stokes equations (NSEs).
• This limitation is analytically demonstrated in channel flow, highlighting the need for improved numerical treatments.

Purpose of the Study:

• To develop and validate modifications to the IBM for accurate velocity gradient calculation within diffused solid-fluid interfaces.
• To enhance the enforcement of no-slip boundary conditions in IBM simulations.

Main Methods:

• A single-sided force distribution kernel is proposed to confine boundary forces to the solid region, restoring NSEs in the fluid domain.
• A novel, computationally inexpensive force amplification technique is introduced to improve no-slip boundary enforcement efficiency.
• These methods are tested in both laminar and turbulent flow regimes.

Main Results:

• The single-sided kernel correctly computes velocity gradients near solid surfaces, unlike standard IBM.
• The force amplification technique significantly reduces iterative requirements for accurate boundary condition enforcement.
• Both proposed methods decrease numerical errors in flow velocity and hydrodynamic forces.

Conclusions:

• The single-sided force kernel and force amplification technique offer significant improvements over standard IBM for simulating flows with diffused interfaces.
• These advancements lead to more accurate velocity gradient calculations and efficient boundary condition enforcement.
• The proposed methods are effective in both laminar and turbulent flow scenarios.