Introduction. Basic Equations. Approximations to Derivatives. Ordinary Differential Equations. The Explicit Method. Boundary Conditions. Unequal Intervals. The Commonly Used Implicit Methods. Other Methods. Adsorption. Effects Due to Uncompensated Resistance and Capacitance. Two-Dimensional Systems. Convection. Performance. Programming. Simulation Packages. Some Mathematical Proofs. Useful Procedures. Example Programs.

Digital Simulation in Electrochemistry

Boundary-fitted coordinate systems for numerical solution of partial differential equations—A review

An evaluation of upwind and central difference approximations by a study of recirculating flow

On the use of nonuniform grids in finite-difference equations

The linear stability of Hagen-Poiseuille flow (Poiseuille pipe flow) with superimposed rigid rotation against small three-dimensional disturbances is examined at finite and infinite axial Reynolds numbers. The neutral curve, which is obtained by numerical solution of the system of perturbation equations (derived from the Navier-Stokes equations), has been confirmed for finite axial Reynolds numbers by a few simple experiments. The results suggest that, at high axial Reynolds numbers, the amount of rotation required for destabilization could be small enough to have escaped notice in experiments on the transition to turbulence in (nominally) non-rotating pipe flow.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112076001304

H. J. Crowder

Papers

Errors in the use of nonuniform mesh systems

On the stability of Poiseuille flow in a pipe