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Solving the Incompressible Surface Stokes Equation by Standard Velocity-Correction Projection Methods.

Yanzi Zhao1, Xinlong Feng1

  • 1College of Mathematics and System Sciences, Xinjiang University, Urumqi 830017, China.

Entropy (Basel, Switzerland)
|July 8, 2023
PubMed
Summary
This summary is machine-generated.

This study presents a numerical algorithm for Stokes equations on curved surfaces, enhancing accuracy for fluid dynamics simulations. The method effectively handles tangential velocity conditions using finite elements and time discretization schemes.

Keywords:
incompressible Stokes equation for surfacesmixed finite element pairpenalty termstandard velocity correction projection method

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Area of Science:

  • Computational fluid dynamics
  • Numerical analysis
  • Partial differential equations

Background:

  • Stokes equations model slow, viscous fluid flow.
  • Solving these equations on curved surfaces presents unique challenges.
  • Existing numerical methods may lack efficiency or accuracy for complex geometries.

Purpose of the Study:

  • To develop and analyze an effective numerical algorithm for the Stokes equation on curved surfaces.
  • To ensure accurate modeling of fluid flow in complex, non-planar domains.
  • To provide a robust computational tool for fluid dynamics research.

Main Methods:

  • Velocity-pressure decoupling using a standard velocity correction projection method.
  • Introduction of a penalty term to enforce tangential velocity conditions.
  • Discretization in time using first-order backward Euler and second-order BDF schemes.
  • Spatial discretization employing the mixed finite element pair (P2,P1).

Main Results:

  • The proposed numerical algorithm demonstrates accuracy and effectiveness.
  • Stability analysis of both backward Euler and BDF time discretization schemes was performed.
  • Numerical examples validated the method's performance on curved surfaces.

Conclusions:

  • The presented numerical algorithm is effective for solving Stokes equations on curved surfaces.
  • The combination of projection method, penalty term, and finite elements provides a robust solution.
  • The study offers a reliable computational approach for fluid dynamics problems involving curved geometries.