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Adaptive mesh refinement techniques for the immersed interface method applied to flow problems.

Zhilin Li1, Peng Song

  • 1Center for Research in Scientific Computation & Department of Mathematics, North Carolina State University, Raleigh, NC 27695, USA.

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Summary
This summary is machine-generated.

This study introduces an adaptive mesh refinement strategy for the Immersed Interface Method, enhancing simulations of fluid flow with moving interfaces. The new method improves accuracy and efficiency for complex fluid dynamics problems.

Keywords:
Adaptive mesh refinement methodNavier-Stokes equationsStokes equationsbubble deformationimmersed interface methodlevel set methodsurface tension

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Area of Science:

  • Computational fluid dynamics
  • Numerical analysis
  • Fluid mechanics

Background:

  • Simulating fluid flow with moving interfaces presents significant computational challenges.
  • Existing methods often struggle with accuracy and efficiency when interfaces change dynamically.
  • Adaptive mesh refinement (AMR) is a powerful technique for improving computational efficiency in such problems.

Purpose of the Study:

  • To develop and validate an adaptive mesh refinement strategy for the Immersed Interface Method (IIM) applied to fluid flow problems with moving interfaces.
  • To extend the AMR-IIM approach previously developed for elliptic problems to more general flow scenarios.
  • To introduce a novel area-preserving strategy for level set methods used in interface tracking.

Main Methods:

  • The Immersed Interface Method (IIM) is employed to handle interface complexities within a Cartesian grid framework.
  • Adaptive Mesh Refinement (AMR) is implemented within a narrow band around the interface (defined by the level set function φ) to locally increase mesh resolution.
  • The method is validated using Stokes and Navier-Stokes equations, incorporating exact solutions and dynamic interface behaviors like surface tension-driven motion and bubble deformation.

Main Results:

  • The developed AMR-IIM strategy effectively handles moving interfaces in fluid flow simulations.
  • Validation against exact solutions and complex scenarios demonstrates the accuracy and robustness of the proposed method.
  • The new area-preserving strategy for level set methods shows promise for improved interface representation.

Conclusions:

  • The adaptive mesh refinement strategy for the Immersed Interface Method provides an efficient and accurate approach for simulating fluid dynamics with moving interfaces.
  • The method is suitable for a range of flow problems, including those driven by surface tension and involving complex interface deformations.
  • The proposed area-preserving level set strategy offers a valuable addition to numerical methods for interface tracking.