Arnaud G. Malan

A matrix-free, implicit, incompressible fractional-step algorithm for fluid-structure interaction applications

In this paper we detail a fast, fully-coupled, partitioned fluid-structure interaction (FSI) scheme. For the incompressible fluid, new fractional-step algorithms are proposed which make possible the fully implicit, but matrix-free, parallel solution of the entire coupled fluid-solid system. These algorithms include artificial compressibility pressure-poisson solution in conjunction with upwind velocity stabilisation, as well as simplified pressure stabilisation for improved computational efficiency. A dual-timestepping approach is proposed where a Jacobi method is employed for the momentum equations while the pressures are concurrently solved via a matrix-free preconditioned GMRES methodology. This enables efficient sub-iteration level coupling between the fluid and solid domains. Parallelisation is effected for distributed-memory systems. The accuracy and efficiency of the developed technology is evaluated by application to benchmark problems from the literature. The new schemes are shown to be efficient and robust, with the developed preconditioned GMRES solver furnishing speed-ups ranging between 50 and 80.

Thermal characterisation of rectangular cooling shapes in solids

Purpose – This paper aims to investigate thermal geometric optimisation of rectangular heat conductive cooling structures within solid heat‐generating media for the purpose of minimising peak temperatures and enabling optimum use of spatial volume within integrated power electronics.Design/methodology/approach – A vortex‐centred finite volume numerical solver was developed, employing a fully implicit solution algorithm to obtain 3D temperature distributions. By comparing the peak temperatures obtained for a wide range of related cases, optimised cross‐sectional shapes for particular input conditions were obtained.Findings – Optimum shapes are dependent on seven identified parameters. In cases where a low percentage of volume is occupied by cooling structures, a high tendency exists for continuous thin cooling layers, as opposed to discrete rectangular cooling inserts, to present the best thermal behaviour. At higher volume percentages, the opposite is true.Practical implications – The reduced dimensions o...

A weakly compressible free-surface flow solver for liquid-gas systems using the volume-of-fluid approach

This paper presents a weakly compressible volume-of-fluid formulation for modelling immiscible high density ratio two-fluid flow under low Mach number conditions. This follows findings of experimental analyses that concluded the compressibility of the gas has a noteworthy effect on predicted pressure loads in liquid-gas flow in certain instances. With the aim of providing a more accurate numerical representation of dynamic two-fluid flow, the solver is subsequently extended to account for variations in gas densities. A set of governing equations is proposed, which accounts for the compressible properties of the gas phase in a manner which allows for a computationally efficient numerical simulation. Furthermore, the governing equations are numerically expressed so that they allow for large variations in the material properties, without introducing notable non-physical oscillations over the interface. For the discretisation of the governing equations an edge-based vertex-centred finite volume approach is followed. The developed solver is applied to various test cases and demonstrated to be efficient and accurate.

A flow network formulation for compressible and incompressible flow

Purpose – One‐dimensional pipe network flow analysis can be used in many applications to satisfactorily solve various engineering problems. The paper aims to focus on this.Design/methodology/approach – A hybrid nodal method is detailed, which solves the pressure field prior to the elemental flows, and models both compressible gas and incompressible liquid and gas flows.Findings – The results obtained by the algorithm were verified against a number of published benchmark flow problems. The methodology was found to yield accuracy similar or improved, compared with that of others, while being applicable to both incompressible liquid and compressible gas flows. Convergence performance was found to be similar to other hybrid techniques.Originality/value – All flows are modelled via a single governing equation set. In the case of incompressible flow, the method is capable of dealing with both constant and variable cross‐sectional area ducts. The latter includes geometrically complex pipes such as sudden expansions.

Hybrid Finite-Volume Reduced-Order Model Method for Nonlinear Aeroelastic Modeling

A fully coupled partitioned fluid–structure interaction technology is developed for transonic aeroelastic structures undergoing nonlinear displacements. The Euler equations, written in an arbitrary Lagrangian–Eulerian coordinate frame, describe the fluid domain, whereas the structure is represented by a quadratic modal reduced-order model. A Runge–Kutta dual time-stepping method is employed for the fluid solver, where three upwind schemes are considered, viz., Advection Upwind Splitting Method plus-up, Harten-Lax-van Leer with Contact, and Roe schemes. The Harten-Lax-van Leer with Contact implementation is found to offer a superior balance between efficiency and robustness. The developed fluid–structure interaction technology is applied to modeling transonic flutter, and the quadratic reduced-order model is demonstrated to offer dramatic improvements in accuracy over the more conventional linear method.

An artificial compressibility method for buoyancy‐driven flow in heterogeneous saturated packed beds

Purpose – The purpose of this paper is to focus on modeling buoyancy driven viscous flow and heat transfer through saturated packed pebble‐beds via a set of homogeneous volume‐averaged conservation equations in which local thermal disequilibrium is accounted for.Design/methodology/approach – The local thermal disequilibrium accounted for refers to the solid and liquid phases differing in temperature in a volume‐averaged sense, which is modeled by describing each phase with its own governing equation. The partial differential equations are discretized and solved via a vertex‐centered edge‐based dual‐mesh finite volume algorithm. A compact stencil is used for viscous terms, as this offers improved accuracy compared to the standard finite volume formulation. A locally preconditioned artificial compressibility solution strategy is employed to deal with pressure incompressibility, whilst stabilisation is achieved via a scalar‐valued artificial dissipation scheme.Findings – The developed technology is demonstra...

An AMG strategy for efficient solution of free-surface flows

Purpose – An area of great interest in current computational fluid dynamics research is that of free-surface modelling (FSM). Semi-implicit pressure-based FSM flow solvers typically involve the solution of a pressure correction equation. The latter being computationally intensive, the purpose of this paper is to involve the implementation and enhancement of an algebraic multigrid (AMG) method for its solution. Design/methodology/approach – All AMG components were implemented via object-oriented C++ in a manner which ensures linear computational scalability and matrix-free storage. The developed technology was evaluated in two- and three-dimensions via application to a dam-break test case. Findings – AMG performance was assessed via comparison of CPU cost to that of several other competitive sparse solvers. The standard AMG implementation proved inferior to other methods in three-dimensions, while the developed Freeze version achieved significant speed-ups and proved to be superior throughout. Originality/...

Free-Surface Modelling Technology for Compressible and Violent Flows

This study presents the development of novel modelling technology for compressible and violent free-surface ows, where the new technology aims to extend the capabilities of existing FSM formulations. For the purpose of this study the volume-of-uid (VOF) method is extended in two ways: Firstly, we aim to improve on the accuracy of existing free-surface interface capturing schemes, and secondly, a newly developed weakly compressible formulation is introduced. The proposed interface capturing formulation reduces the degree of numerical smearing, while maintaining the integrity of the interface shape. It involves combining the approaches of blended higher-resolution discretisation and adding an articial compressive term in a manner which retains the strength of each. The weakly compressible formulation proposes an altered governing equation set which accurately accounts for large variance in gas density at low Mach numbers and may be solved at little additional computational cost. All governing equations are discretized via an unstructured edge-based vertex centred nite volume method, and solved via a parallel implicit solver.

A hybrid framework for coupling arbitrary summation-by-parts schemes on general meshes

We develop a general interface procedure to couple both structured and unstructured parts of a hybrid mesh in a non-collocated, multi-block fashion. The target is to gain optimal computational effi ...

Numeric Analysis of Temperature Distribution in Man using a 3D Human Model

Premortem three-dimensional body temperature is the basis on which post-mortem cooling commences. Thermo-numeric analysis of post-mortem cooling for death-time calculation applies pre-mortem three-dimensional body temperature as initial conditions; therefore, an accurate determination of this distribution is important. To date, such prediction is not performed. This paper presents a thermo-numeric analysis method of predicting premortem three-dimensional body temperature in man, to be applied in thermo-numeric analysis of the post-mortem interval using the finite-difference time-domain method. The method applied a Pennes BioHeat Equation modified to linearize organ metabolic and blood flow rates with temperature in a transient thermo-numeric analysis scheme to predict naked three-dimensional temperatures of an MRI-built, 3D human model having 247 segmented organs and 58 categories of material properties under chosen boundary conditions. Organ metabolic heat and blood perfusion rates appropriate for a chosen pre-mortem physical activity, and known organ physical and thermal properties, were assigned to each organ. A steady-state temperature equilibration occurred after 8400 seconds. Predicted organ temperatures were topographically inhomogeneous. Skin temperatures varied between 20.5°C and 42.5°C, liver capsule temperatures were lower than parenchymal, and rectal luminal temperature were uniform.