Simplified Procedure for Numerically Approximate Jacobian Matrix Generation in Newton's Method for Solving the Navier-Stokes Equations. G.U. Aero Report 9320

Xu, X. and Richards, B.E. (1993) Simplified Procedure for Numerically Approximate Jacobian Matrix Generation in Newton's Method for Solving the Navier-Stokes Equations. G.U. Aero Report 9320. Technical Report. Department of Aerospace Engineering, University of Glasgow.

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Abstract

Since residual vector in a control volume is the linear combination of inviscid and viscous flux vectors on its all edges when a finite volume method is used, we can use flux vectors instead of residual vector in the formulation of generating Jacobian matrix elements. In the actual numerical calculation, after setting a variable perturbation in a control volume, we only calculate these flux vectors that according to the analysis they will change values because the variable perturbation, therefore we don't need to calculate all flux vectors which will compose of the residual vector. The new procedure decrease the amount of computation greatly, and also reduces the extent of the physical state variables used. For parallel computation the new procedure will short the storage of physical state variables in each subdomain.

Item Type:Research Reports or Papers (Technical Report)
Status:Published
Glasgow Author(s) Enlighten ID:Richards, Professor Bryan
Authors: Xu, X., and Richards, B.E.
College/School:College of Science and Engineering > School of Engineering > Aerospace Sciences
Publisher:Department of Aerospace Engineering, University of Glasgow
Copyright Holders:Copyright © 1993 Department of Aerospace Engineering, University of Glasgow
Publisher Policy:Reproduced with the permission of the Department

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