A provably stable and high-order accurate finite difference approximation for the incompressible boundary layer equations

Mojalefa P. Nchupang, Arnaud G. Malan, Fredrik Laurén, Jan Nordström

Research output: Contribution to journalArticlepeer-review

Abstract

In this article we develop a high order accurate method to solve the incompressible boundary layer equations in a provably stable manner. We first derive continuous energy estimates, and then proceed to the discrete setting. We formulate the discrete approximation using high-order finite difference methods on summation-by-parts form and implement the boundary conditions weakly using the simultaneous approximation term method. By applying the discrete energy method and imitating the continuous analysis, the discrete estimate that resembles the continuous counterpart is obtained proving stability. We also show that these newly derived boundary conditions removes the singularities associated with the null-space of the nonlinear discrete spatial operator. Numerical experiments that verifies the high-order accuracy of the scheme and coincides with the theoretical results are presented. The numerical results are compared with the well-known Blasius similarity solution as well as that resulting from the solution of the incompressible Navier–Stokes equations.

Original languageEnglish
Article number106073
JournalComputers and Fluids
Volume267
DOIs
Publication statusPublished - 15 Dec 2023

Keywords

  • Boundary conditions
  • Boundary layer equations
  • High order methods
  • Incompressible Navier–Stokes equations
  • Simultaneous approximation terms
  • Summation-by-parts

ASJC Scopus subject areas

  • General Computer Science
  • General Engineering

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