A C²‐continuous high‐resolution upwind convection scheme

Abstract

SUMMARY A bounded upwinding scheme for numerical solution of hyperbolic conservation laws and Navier–Stokes equations is presented. The scheme is based on convection boundedness criterion and total variation diminishing stability criteria and developed by employing continuously differentiable functions. The accuracy of the scheme is verified by assessing the error and observed convergence rate on 1‐D benchmark test cases. A comparative study between the new scheme and conventional total variation diminishing/convection boundedness criterion‐based upwind schemes to solve standard nonlinear hyperbolic conservation laws is also accomplished. The scheme is then examined in the simulation of Newtonian and non‐Newtonian fluid flows of increasing complexity; a satisfactory agreement has been observed in terms of the overall behavior. Finally, the scheme is used to study the hydrodynamics of a gas‐solid flow in a bubbling fluidized bed. Copyright © 2013 John Wiley & Sons, Ltd.

Interaction between Shock Waves Travelling in the Same Direction

“…Supersonic flows are complex numerical simulation problems. The problem regarding the regular or Mach reflection of a shock wave from a wall is used in many studies to establish the accuracy of different schemes and the performance of numerical methods [21][22][23][24][25].…”