1 

The N2 gateway project in Cape Town: relocation or forced removal?

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2 

From Ireland to Cape Town. An exploration into the benefits of comparative housing research for NGOs in
the global South

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3 

Validation of the interfaceGMRES(R) solution method for fluidstructure interactions
The numerical solution of fluidstructure interactions with the customary subiteration method incurs numerous deficiencies. We validate a recently proposed solution method based on the conjugation of subiteration with a NewtonKrylov method, and demonstrate its superiority and beneficial characteristics.

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4 

Implicitexplicit RungeKutta method for combustion simulation
New high order implicitexplicit RungeKutta methods have been developed and implemented into a finite volume code to solve the NavierStokes equations for reacting gas mixtures. The resulting nonlinear systems in each stage are solved by Newtons method. If only the chemistry is treated implicitly, the linear systems in each Newton iteration are simple and solved directly. If in addition certain convection or diffusion terms are treated implicitly as well, the sparse linear systems in each Newton iteration are solved by preconditioned GMRES. Numerical simulations of deflagrationtodetonation transition (DDT) show the potential of the new time integration for computaional combustion.

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5 

New method for solving the NavierStokes equations with artificial relations between variations of quantities, applied at nearest nodes
With the use of the Newton method, a new numerical method previously published [1] for solving the threedimensional NavierStokes equations, is theoretically proved for the most simple case of onedimensional acoustic equations. The convergence of iteration scheme is proved. In this paper, we also recall some theoretical and numerical results presented earlier in [1]. The gradient of internal energy (see [1]) has to be redefined. This yielded in [1] that, along with descending temperature of internal walls, some small variations of balance of mass arose within the flow of a gas heated from its motion along tube walls. The author succeeded [1] in achieving the maximal time step Dtmax=h/uflow (h is the average size of cell, uflow stands for the flow velocity) along with the condition that, on every step, the required computation time exceeds approximately 6 times the time necessary for computation via an explicit scheme. Every step requires a number of arithmetic operations of order of N; here N is the number of nodes and cells. The stability and velocity of convergence were estimated in a numerical experience. Satisfactory correlation is obtained between the analytic and computed balances of mass in a tube for a given wall temperature dependence. Next, briefly, the idea of the method includes an artificial binding of unknowns' corrections at neighbouring nodes or cells; the respective corrections are determined not via solving bounded system of equations, but in a way directly based on the residual of equation for the corresponding unknown at either a node or a cell. A staggered arrangement of variables is used, this means that the pressure, density, and internal energy are located at the usual cell centres, whereas the velocity vectors are positioned at the displaced cell centres which are the vertices of usual cells. The threedimensional NavierStokes equations are solved via the Newton iteration procedure. The initial guesses are taken for the time t + Dt as known values for time t, and the time step Dt is chosen with the requirement to provide the convergence within an approximately given number of iterations; then the divergence will be avoided due that restriction of time step. The introduction of artificial relations between the variations of quantities at the nearest nodes or cells and the use of approximate equality with opposite signs of vectors relating the geometric coefficients of both displaced and usual cells, make it possible to obtain formulas for correct rates of change of the residuals of equations.

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6 

On the solution of the dieswell problem using an unstructured mesh
Newtontype solution method. Detailed implementation for a model free boundary problem is presented along with the numerical results.

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7 

A Monomial Chaos Approach for Efficient Uncertainty Quantification in Computational Fluid Dynamics
A monomial chaos approach is proposed for efficient uncertainty quantification in nonlinear computational problems. Propagating uncertainty through nonlinear equations can still be computationally intensive for existing uncertainty quantification methods. It usually results in a set of nonlinear equations which can be coupled. The proposed monomial chaos approach employs a polynomial chaos expansion with monomials as basis functions. The expansion coefficients are solved for using implicit differentiation of the governing equations. This results in a decoupled set of linear equations even for nonlinear problems, which reduces the computational work per additional polynomial chaos order to the equivalence of one Newton iteration. The results of the monomial chaos applied to nonlinear advectiondiffusion are compared with results of the perturbation method, the Galerkin polynomial chaos method and a nonintrusive polynomial chaos method with respect to a Monte Carlo reference solution. The accuracy of the monomial chaos can be further improved by estimating additional coefficients using extrapolation.

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8 

Preconditioners for Linearized Discrete Compressible Euler Equations
We consider a NewtonKrylov approach for discretized compressible Euler equations. A good preconditioner in the Krylov subspace method is essential for obtaining an efficient solver in such an approach. In this paper we compare pointblockGaussSeidel, pointblockILU and pointblockSPAI preconditioners. It turns out that the SPAI method is not satisfactory for our problem class. The pointblockGaussSeidel and pointblockILU preconditioners result in iterative solvers with comparable efficiencies.

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9 

A hybrid electromagneticscircuit simulation method exploiting discontinuous Galerkin time domain finite element method
A hybrid electromagnetics (EM)circuit simulation method employing the discontinuous Galerkin finite element time domain method (DGFETD) is developed to model single lumped port networks comprised of both linear and nonlinear elements. The whole computational domain is split into two subsystems. One is the EM subsystem that is analyzed by the DGFETDwhile another is the circuit circuit subsystem that is modeled by the Modified Nodal Analysis method (MNA) to generate a circuit subsystem. The coupling between the EM and circuit subsystems is achieved through a lumped port. Due to the local properties of DGFETD operations, only small coupling matrix equation systems are involved. To solve nonlinear devices, the standard NewtonRaphson method is applied to solve the established nonlinear system equations. Numerical examples are presented to validate the proposed algorithm.

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10 

Analysis of a hybrid pMultigrid method for the discontinuous Galerkin discretisation of the Euler equations
A hybrid implicit and explicit pMultigrid iteration strategy for the discretisation of the steady Euler equations with the discontinuous Galerkin finite element method is presented. The implicit strategy consists of an inexact damped Newton iteration, using an ILU(0)preconditioned GMRES method for the solution of the linear system. Since the size of the preconditioner grows quadratically (2D) / cubically (3D) with the interpolation order, this method becomes impractical for moderate to high order interpolations. Therefore the implicit method is embedded in a FAS multilevel iteration scheme, which is based on successive interpolation spaces. The implicit solver is only on the lowest order interpolation spaces, while on the higher order levels a cheap explicit method is used. The fast convergence of the solution on the noncoarsened levels speeds up the convergence of the multilevel iterations considerably. The interlevel transfer operations are based on L2 projections for the solutions and on a reformulation of the variational problem itself for the residual. These operators are straightforward to implement and localized per element. The convergence of the pMultigrid twocycle algorithm using those operators is investigated theoretically and experimentally.

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11 

Numerical Simulation of Flow over an Axisymmetric body in Free Flight
Flow field around a projectile after thrust has been stopped and in inertia flight is studied numerically by a finite difference scheme. This study aims at clarifying the mechanism of free flight, which is generated and developed by rotation of body and gravity. Among two types of projectiles concerned a threedimensional flow around the slender body, such as aircraft body, rocket .causes drastic variation with high angle of attack and has considerable influence on the aerodynamic behavior. The flow over a paraboloidalnose cylinder at pitching rotation is considered with inertia translating motion and the flow symmetry assumption . Another example is a oblate spheroid, and in these examples the initial condition is the flow at steady ‘flight’. In present numerical study coordinate system fixed on the body ,with noninertial frame of reference, which yields additional terms in Navier Stokes equation. The dualtime pseudo compressibility code is applied for incompressible flow. The Newton’s 2nd law is used with the balance of aerodynamic force and gravity together with angular momentum equation. For the slender body the initial incidence angle is horizontal or 40deg. For the spheroid the initial motion is set either upwardi: counter to gravitydirection or downward one. For Reynolds numbers lower than 10000, the behavior of flow field and varying incidence angle will be discussed as well asthe trajectory of body.

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12 

A monolithic FEM solver for an ALE formulation of fluidstructure interaction with configuration for numerical benchmarking
We investigate a monolithic algorithm to solve the problem of time dependent interaction between an incompressible viscous fluid and an elastic solid. The continuous formulation of the problem and its discretization is done in a monolithic way, treating the problem as one continuum. The Q2/P1 finite elements are used for the discretization and an approximate Newton method with coupled multigrid linear solver is developed for solving the equations. We discuss possible efficient strategies of setting up the resulting system and its solution. A 2dimensional configuration is presented to test the developed method. It is based on the older successful DFG benchmark flow around cylinder for incompressible laminar fluid flow. Similar to this older benchmark we consider the flow to be incompressible and in the laminar regime. The structure is allowed to be compressible or incompressible and the deformations of the structure are periodic and significant in terms of displacement. This configuration can be used to compare different numerical methods and code implementations for the fluidstructure interaction problem qualitatively and particularly quantitatively with respect to efficiency and accuracy of the computation.

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13 

Simulation of lowMachnumber flow using a fullycoupled implicit residualdistribution method
An effective approach is presented for the numerical solution of the equations governing steady laminar and turbulent flow, heat and mass transfer at low Mach number. The approach adopted combines a compact and accurate discretization using the residualdistribution (RD) approach with a fullycoupled implicit solution procedure. The system RD approach adopted employs genuinelymultidimensional upwinding to achieve accurate and stable discrete equations on a highly compact computational stencil. This combines very naturally with the fullyimplicit coupled solution procedure for which the number of nonlinear iterations required is essentially independent of the grid size. This contrasts with other widely used segregated approaches in which the pressurevelocity system is discretized and solved as a set of scalar equations. A further key distinction from many other implicit methods is that the compact nature of the discretization allows the full convection and diffusion terms in all equations to be treated implicitly without any form of deferred correction. The code developed solves the 2D, axisymmetric and 3D NavierStokes equations in incompressible or weaklycompressible form on unstructured grids of triangles or tetrahedra. The RD form of the system LaxWendroff scheme is applied to the convection and pressure terms while the viscous terms are treated using the Galerkin finiteelement method. The system scheme for convection provides natural stabilization, allowing a collocated variable arrangement to be used. Convection terms in scalar equations are treated using scalar multidimensional RD schemes such as the N and PSI schemes, both of which are positive. The discrete equation system is solved using a fullycoupled implicit approach based on Picard/Newton linearization with the linear system solved using standard Krylov subspace methods (e.g. GMRES or BiCGStab) with ILU(0) preconditioning. A number of practical issues relating to the solution procedure have been investigated including parallelization and equation segregation. A domain decomposition method has been developed for the treatment of large problems using a multiplicativeSchwarz approach with arbitrary interblock overlap. The approach has been extensively validated on a number of 2D, axisymmetric and 3D test cases, with and without heat and mass transfer. This has included direct comparisons with commercial unstructured flow solvers with very promising results  showing equivalent levels of accuracy but reduced computational times and less sensitivity to grid quality. Examples of the validation and application of the method are presented.

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