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

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

Applications and Parallel Implementation of the Continuation Method for a Fully Implicit N-S Solver. G.U. Aero Report 9416

No abstract available

Application of the Highest Order Finite Difference Scheme to Solve Incompressible Navier-Stokes Equations. G.U. Aero Report 9226

This paper introduces a global method of the highest order finite difference scheme for the discretization of any order derivative. The weighting coefficients in this scheme can be deteraiined by a simple algebraic formulation or by a recurrence relationship. A multi-domain technique was also presented for treating more complex problems. Application of this scheme to solve 2D incompressible Navier-Stokes equations showed that accurate numerical results can be achieved using just a few grid points and requiring much less computational effort and storage

Validation of the New Version PNS3DT Code. G.U. Aero Report 9401.

In this Study, the PNS3DT code developed in the University of Glasgow to solve steady compressible parabolized Navier-Stokes equations with Baldwin-Lomax turbulence model is updated. The choice of primitive variables in the numerical scheme, different wall temperature conditions as well as the effect of different grid stretching strategies are tested in detail. Excellent agreement between the numerical and experimental results is observed. Thus, the code could provide a powerful tool to predict the aerodynamics characteristics on the ogive cylinder surface and to simulate the complicate flow structures around the cylinder

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

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

The Morphology of the Tasmantid Seamounts: Interactions Between Tectonic Inheritance and Magmatic Evolution

No abstract available

Application of PMB2D to Axisymmetric Flows. Department of Aerospace Engineering report 9812

This report describes how the two-dimensional planar flow solver PMB2D has been modified for axisymmetric flows. The equations describing axisymmetric flows are derived. The issue of conservation is discussed. The modified linear system arising at each implicit time step is detailed. Finally, results for inviscid, laminar and turbulent flow test cases are presented

Towards Automatic Multiblock Topology Generation. G.U. Aero Report 9826

The need for automation of the multiblock grid generation process is discussed. A new approach to automatically process a multiblock topology in order to prepare it for the grid generation process is described. The method is based on a cost function which attempts to model the objectives of the skilled grid generation software user who at present performs the task of block positioning and shaping in an interactive manner. A number of test cases are examined. It is also suggested that an existing unstructured mesh generation method could be adopted as an initial topology generation tool. Further work towards creating a fully automatic grid generation tool and extension into three dimensions are discussed briefly

Parallelization of Explicit and Fully Implicit Navier-Stokes Solutions for Compressible Flows. G.U. Aero Report 9236

The paper describes two studies involved with the parallelisation of algorithms for the numerical calculation of hypersonic viscous flows over generic vehicle configurations by solving the Navier-Stokes equations. One involved a scalable explicit formulation that achieved high parallel efficiency on 32 processors of an Intel iPSC860 Hypercube when calculating the 3-dimensional flow over a blunt delta wing at high incidence, the other involved a fully implicit formulation using a Newton-like procedure with a GMRES solver with pre-conditioning when high efficiency was achieved when run on 8 transputers of a Meiko Computing Surface computer in order to calculate the flow over a cone at high incidence. This latter approach, although more complex, has potential in providing more rapid convergence characteristics, hence efficiency, than the explicit scheme. High order upwind discretisation was used in each case in order to achieve high resolution of important shock and viscous phenomenon within the flow field. The work reported contributes to the aim of a wider programme of work, a summary of which is included, to provide the computational tools to calculate accurately and efficiently steady and unsteady viscous compressible flows over complex aerospace configurations

Unfactored Multiblock Methods: Part I - Initial Method Development. G.U. Aero Report 9511

The use of implicit multiblock methods is discussed and an unfactored method based on a conjugate gradient type solution is described. Preconditioners appropriate to multiblock are considered along with future extensions to parallel computing