Reduced Navier-Stokes Equations Near a Flow Boundary

Abstract

We derive a hierarchy of PDEs for the leading-order evolution of wall-based quantities, such as the skin-friction and the wall-pressure gradient, in two-dimensional fluid flows. The resulting Reduced Navier-Stokes (RNS) equations are defined on the boundary of the flow, and hence have reduced spatial dimensionality compared to the Navier-Stokes equations. This spatial reduction speeds up numerical computations and makes the equations attractive candidates for flow-control design. We prove that members of the RNS hierarchy are well-posed if appended with boundary-conditions obtained from wall-based sensors. We also derive the lowest-order RNS equations for three-dimensional flows. For several benchmark problems, our numerical simulations show close finite-time agreement between the solutions of RNS and those of the full Navier-Stokes equations.

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Document Details

Document Type
Technical Report
Publication Date
Aug 04, 2005
Accession Number
ADA458888

Entities

People

  • G. B. Jacobs
  • G. Haller
  • J. S. Hesthaven
  • M. S. Kilic

Organizations

  • Massachusetts Institute of Technology

Tags

Communities of Interest

  • Ground and Sea Platforms
  • Sensors

DTIC Thesaurus Topics

  • Boundaries
  • Boundary Layer
  • Channel Flow
  • Equations
  • Hypervelocity Flow
  • Incompressible Flow
  • Layers
  • Mathematics
  • Mechanical Engineering
  • Navier Stokes Equations
  • Pressure Gradients
  • Pressure Measurement
  • Skin Friction
  • Steady State
  • Stratified Fluids
  • Three Dimensional
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Fluid Mechanics and Fluid Dynamics.