A Fully Coupled, Implicit, Numerical Scheme for Laminar and Turbulent Parabolic Flows

Abstract

A fully coupled, implicit, numerical scheme has been developed for solving highly stiff systems of parabolic conservation equations. The finite‐domain equations are formed by integration of the governing conservation equations, expressed in vector notation, over control volumes. The central idea is to put the discretized vector equations as Differential/Algebraic equations (DAE) in the context of numerically solving a system of stiff ordinary differential equations. One of the benefits of the present numerical method is that the Jacobian matrix retains its banded property and thus the problems related to computer storage are eliminated. The mathematical interface that the code employs is a computer program that is most efficient for solving the stiff equations usually found in chemical kinetics. The method has shown good convergence rate and numerical stability. The mathematical formulation is capable of modelling laminar and turbulent flows. Two study cases are considered in this work to illustrate the applicability of the numerical method. Case one corresponds to a numerical simulation of a laminar non‐premixed methane–air flame. The chemical processes are described with a four‐step reduced mechanism that derives from a larger mechanism with twenty‐five reaction steps. The predicted velocity, temperature, and mole fractions of the confined laminar round‐jet flame investigated here are compared with experimental data taken from the literature. The versatility of the present solver for predicting high Reynolds number flows is demonstrated by simulating an isothermal turbulent air jet, labelled as case two. A standard two‐equation turbulence model is used to simulate the turbulence processes. The analytical velocity distribution for a turbulent submerged jet is used as a benchmark to test the performance of the model for turbulent jets. © 1997 by John Wiley & Sons, Ltd.

A new simple method of implicit time integration for dynamic problems of engineering structures

“…Many approaches have been established to solve different dynamic problems, such as structure, fluid flowing, and multi-rigid-body systems [3][4][5][6][7][8][9][10][11][12]. They are mainly classified into two categories: explicit and implicit algorithms.…”