Analysis of microwave induced natural convection in a single mode cavity (Influence of sample volume, placement, and microwave power level)

The heating of water layer using microwave oven with a rectangular waveguide has been studied both numerically and experimentally. The mathematical model is validated with the experimental data. The transient Maxwell’s equations are solved by using the Finite Difference Time Domain (FDTD) method to describe the electromagnetic field inside the waveguide and sample. The temperature profile and velocity field within sample are determined by the solutions of the momentum, energy and Maxwell’s equations. In this study, the effects of physical parameters, e.g. microwave power level, placement of sample inside the waveguide, volume of sample, are studied. The distribution of electric field, temperature profile and velocity field are presented in details. The results show good agreement between simulation results and experimental data. Conclusively, the mathematical model presented here correctly explains the phenomena of microwave heating of water layer.     

A hybrid technique for computing the power distribution generated in a lossy medium during microwave heating

Over the years researchers in the field of computational electromagnetics (CEM) have investigated and explored a number of different techniques to resolve electromagnetic fields inside waveguide and cavity structures. The equations that govern the fundamental behaviour of electromagnetic wave propagation in such structures are Maxwell's equations. In the literature, a number of different techniques have been employed to solve these equations and out of these methods, the classical finite-difference time-domain (FD-TD) scheme, which uses a staggered time and space discretisation, is the most well-known and widely used. However, this scheme is complicated to implement on an irregular computational domain using unstructured meshes.This research work builds upon previous work undertaken for a waveguide, where a coupled method was introduced for the solution of the governing electromagnetic equations. In that work, the free-space component of the solution was computed in the time-domain, whilst the power distribution in the load was resolved using the frequency dependent electric field Helmholtz equation. This methodology resulted in a time-frequency domain hybrid scheme. In this paper, the hybrid method has been tested further for both waveguide and cavity configurations that are loaded with a lossy dielectric material. Numerical tests highlight both the accuracy and computational efficiency of the proposed hybrid strategy for predicting the power distribution generated during microwave heating processes. The accuracy of the hybrid scheme is gauged by direct comparison with the FD-TD numerical solutions and previously published thermal images.     

Numerical Simulation of Heat Loads in a Cryogenic H2/O2 Rocket Combustion Chamber

A Finite Element solver for a coupled simulation of fluid and structure in an axisymmetric domain is presented. The method employs an explicit solution of the flow and structure variables. The computational domain of the fluid is discretised by unstructured triangles and rectangles while the sturcture domain is discretised by unstructured triangles only. For the purpose of code validation the solution of in total three test cases are shown. One test case deals with the structure only while the other two simulate heat transfer problems with a defined temperature distribution along a boundary wall and coupled conditions. Finally the code is used to simulate the heat load in a cryogenic H₂/O₂ rocket combustion chamber.     

三维横向流体诱发直管振动的数值模拟

基于有限体积法和有限元法,结合动网格控制技术,建立了横向流体作用下三维弹性直管流致振动计算的数值模型,实现了计算结构动力学与计算流体力学之间的联合仿真．首先,通过对刚性管的静止绕流计算,研究了网格离散方式和不同湍流模型对圆柱类结构静止绕流流场特征的影响和预测能力,得到了适用于双向耦合分析的CFD模型;其次,利用基于双向流固耦合方法的流致振动模型,计算并分析了流体力与结构位移间的相位关系,指出流体力与位移间的相位差是由流体力引起的,同时对双向耦合和单向耦合进行了比较分析;最后通过对直管流致振动的数值计算,联合管表面压力、尾流区时均速度、分离角等时均量,分析了尾流区的流场特征.     

The Concept of Dividing Lines/Surfaces for the Finite Difference Element Method (FDEM)

The FDEM (Finite Difference Element Method) is a black‐box solver for the solution of nonlinear systems of elliptic and parabolic PDEs [1]. We use a FDM of arbitrary consistency order on an unstructured FEM mesh. We compute a reliable error estimate which we also use for an automatic consistency order control and mesh refinement. By dividing lines (2‐D) or dividing surfaces (3‐D) we extend this method for the uniform solution over coupled domains.     

Non-Newtonian phase-change heat transfer of nano-enhanced octadecane with mesoporous silica particles in a tilted enclosure using a deformed mesh technique

In the present study, the melting phase-change heat transfer of nano-enhanced phase-change octadecane by using mesoporous silica particles is investigated in an inclined cavity, theoretically. The presence of mesoporous silica particles induces non-Newtonian effects in the molten octadecane. A phase-change interface-tracking approach, deformed mesh technique, is employed to track the phase-change interface and heat transfer in the cavity. The Arbitrary Lagrangian-Eulerian (ALE) moving mesh technique along with the finite element method is adopted to solve the governing equations for conservation of mass, momentum, and energy during the phase-change process. A re-meshing technique and an automatic time step control approach are employed to control the quality of the deformed mesh and the computed numerical solution. The effect of various mass fractions of nanoparticles and various inclination angles of the enclosure on the heat transfer and phase-change behavior of nano-enhanced octadecane are addressed. The outcome reveals that using the mesoporous silica particles diminish the heat transfer in the enclosure. Although the presence of nanoparticles improved the conductive heat transfer, a reduction in the phase-change heat transfer performance of the enclosure can be observed, which is due to the increase of the viscosity (consistency parameter) of the liquid and suppression of natural convective flows. Moreover, the presence of nanoparticles reduces the latent heat capacity of octadecane as they do not contribute to the phase-change energy storage. Dispersing 5% mass fraction of nanoparticles in octadecane can reduce the heat transfer up to 50% and increase the consistency parameter by three folds. The angle of inclination of the cavity also plays an important role in the heat transfer characteristics. Tilting the cavity by -75° leads to an 80% reduction in the heat transfer.     

Performance comparison of the NWF and DC methods for implementing High-Resolution schemes in a fully coupled incompressible flow solver

This paper reports on the use of the Normalized Weighting Factor (NWF) method and the Deferred Correction (DC) approach for the implementation of High Resolution (HR) convective schemes in an implicit, fully coupled, pressure-based flow solver. Four HR schemes are realized within the framework of the NWF and DC methods and employed to solve the following three laminar flow problems: (i) lid-driven flow in a square cavity, (ii) sudden expansion in a square cavity, and (iii) flow in a planar T-junction, over three grid systems with sizes of 10⁴, 5 × 10⁴, and 3 × 10⁵ control volumes. The merit of both approaches is demonstrated by comparing the computational costs required to solve these problems using the various HR schemes on the different grid systems. Whereas previous attempts to use the NWF method in a segregated flow solver failed to produce converged solutions, current results clearly demonstrate that both methods are suitable for utilization in a coupled flow solver. In terms of CPU efficiency, there is no global and consistent superiority of any method over another even though the DC method outperformed the NWF method in two of the three test problems solved.     

Complex fluid simulations with the parallel tree-based Lattice Boltzmann solver Musubi

We present the open source Lattice Boltzmann solver Musubi. It is part of the parallel simulation framework APES, which utilizes octrees to represent sparse meshes and provides tools from automatic mesh generation to post-processing. The octree mesh representation enables the handling of arbitrarily complex simulation domains, even on massively parallel systems. Local grid refinement is implemented by several interpolation schemes in Musubi. Various kernels provide different physical models based on stream-collide algorithms. These models can be computed concurrently and can be coupled with each other. This paper explains our approach to provide a flexible yet scalable simulation environment and elaborates its design principles and implementation details. The efficiency of our approach is demonstrated with a performance evaluation on two supercomputers and a comparison to the widely used Lattice Boltzmann solver Palabos.     

Fast iterative solver for convection‐diffusion systems with spectral elements

We introduce a solver and preconditioning technique based on Domain Decomposition and the Fast Diagonalization Method that can be applied to tensor product based discretizations of the steady convection–diffusion equation. The method is based on a Robin–Robin interface preconditioner coupled to a fast diagonalization solver which is used to efficiently eliminate the interior degrees of freedom and perform subsidiary subdomain solves. Using a spectral element discretization, we first apply our technique to constant wind problems, and then propose a means for applying the technique as a preconditioner for variable wind problems. We demonstrate that iteration counts are mildly dependent on changes in mesh size and convection strength. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2011     

Parallel multi-frontal solver for p adaptive finite element modeling of multi-physics computational problems

The paper presents a parallel direct solver for multi-physics problems. The solver is dedicated for solving problems resulting from adaptive finite element method computations. The concept of finite element is actually replaced by the concept of the node. The computational mesh consists of several nodes, related to element vertices, edges, faces and interiors. The ordering of unknowns in the solver is performed on the level of nodes. The concept of the node can be efficiently utilized in order to recognize unknowns that can be eliminated at a given node of the elimination tree. The solver is tested on the exemplary three-dimensional multi-physics problem involving the computations of the linear acoustics coupled with linear elasticity. The three-dimensional tetrahedral mesh generation and the solver algorithm are modeled by using graph grammar formalism. The execution time and the memory usage of the solver are compared with the MUMPS solver.     

Aerodynamic optimisation of a hypersonic reentry vehicle based on solution of the Boltzmann–BGK equation and evolutionary optimisation

Over the past decade there has been a surge in the interest, both academic and commercial, in supersonic and hypersonic passenger transport. This paper outlines an original approach for solving the problem of optimal design and configuration of a space vehicle operating in rarefied hypersonic flow. The approach utilises a novel flow solver based on the solution of the Boltzmann–BGK equation. For the first time this solver has been coupled to an evolutionary optimiser to assist in navigation of the unfamiliar hypersonic design space.The Boltzmann–BGK solver is rigorously tested on a number of examples and is shown to handle rarefied gas dynamics examples across a range of length scales. The examples, presented here for the first time, include: a Riemann-type gas expansion problem, drag prediction of a nano-particle and supersonic flow across an aerofoil. Finally the solver is coupled to the evolutionary optimiser Modified Cuckoo Search approach. The coupled solver-optimiser design tool is then used to explore the optimum configuration of the forebody of a generic space reentry vehicle under a range of design conditions.In all examples considered the flow solver produces valid solutions. It is also found that the evolutionary optimiser is successful in navigating the unfamiliar design space.     

A group based solution strategy for multi-physics simulations in parallel

Multi-physics simulation often requires the solution of a suite of interacting physical phenomena, the nature of which may vary both spatially and in time. For example, in a casting simulation there is thermo-mechanical behaviour in the structural mould, whilst in the cast, as the metal cools and solidifies, the buoyancy induced flow ceases and stresses begin to develop. When using a single code to simulate such problems it is conventional to solve each ‘physics’ component over the whole single mesh, using definitions of material properties or source terms to ensure that a solved variable remains zero in the region in which the associated physical phenomenon is not active. Although this method is secure, in that it enables any and all the ‘active’ physics to be captured across the whole domain, it is computationally inefficient in both scalar and parallel. An alternative, known as the ‘group’ solver approach, involves more formal domain decomposition whereby specific combinations of physics are solved for on prescribed sub-domains. The ‘group’ solution method has been implemented in a three-dimensional finite volume, unstructured mesh multi-physics code, which is parallelised, employing a multi-phase mesh partitioning capability which attempts to optimise the load balance across the target parallel HPC system. The potential benefits of the ‘group’ solution strategy are evaluated on a class of multi-physics problems involving thermo-fluid–structural interaction on both a single and multi-processor systems. In summary, the ‘group’ solver is a third faster on a single processor than the single domain strategy and preserves its scalability on a parallel cluster system.     

Hot spot formation in microwave heated ceramic fibres

An analysis of microwave heating of a thin ceramic cylinderin a single mode, highly resonant cavity is presented. Realisticassumptions regarding the effective electrical conductivity,thermal parameters, and physical dimensions are adhered to throughout.Consequently, the model developed herein incorporates most ofdetuning and a local electric feild perturbation on the heatingprocess. The model presented takes the form of a one-dimensionalreaction–diffusion equation which contains a functional.The developement of this equation is the product of a systematicmodelling process that involves S-matrix theory, a small-Biot-numberasymptotic analysis, and a matched asymptotic analysis of anon-standard electromagnetic scattering problem. This equationreveals both the mathematical structure and physical mechanismfor the formation of hot spots. An accurate numerical methodwhich approximates the solution of this equation is presented.The results agree qualitatively with experiments and predictobserved trends.     

Dynamical iteration schemes for coupled simulation in nanoelectronics

In this paper we present an approach to coupled electro–thermal circuit simulation. More precisely we derive from the heat diffusion PDE a thermal element model and we show how it can be included in a standard SPICE–like circuit simulator without significant modifications to the solver structure. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

An adaptive,multilevel scheme for the implicit solution of three‐dimensional phase‐field equations

Phase‐field models, consisting of a set of highly nonlinear coupled parabolic partial differential equations, are widely used for the simulation of a range of solidification phenomena. This article focuses on the numerical solution of one such model, representing anisotropic solidification in three space dimensions. The main contribution of the work is to propose a solution strategy that combines hierarchical mesh adaptivity with implicit time integration and the use of a nonlinear multigrid solver at each step. This strategy is implemented in a general software framework that permits parallel computation in a natural manner. Results are presented that provide both qualitative and quantitative justifications for these choices.© 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010     

Bubble simulations with an interface tracking technique based on a partitioned fluid-structure interaction algorithm

Numerical techniques frequently used for the simulation of one bubble can be classified as interface tracking techniques and interface capturing techniques. Most of these techniques calculate both the flow around the bubble and the shape of the interface between the gas and the liquid with one code. In this paper, a rising axisymmetric bubble is simulated with an interface tracking technique that uses separate codes to determine the position of the gas-liquid interface and to calculate the flow around the bubble. The grid converged results correspond well with the experimental data.The gas-liquid interface is conceived as a zero-mass, zero-thickness structure whose position is determined by the liquid forces, a uniform gas pressure and surface tension. Iterations between the two codes are necessary to obtain the coupled solution of both problems and these iterations are stabilized with a fluid-structure interaction (FSI) algorithm. The flow around the bubble is calculated on a moving mesh in a reference frame that rises at the same speed as the bubble. The flow solver first updates the mesh throughout the liquid domain given a position of the gas-liquid interface and then calculates the flow around the bubble. It is considered as a black box with the position of the gas-liquid interface as input and the liquid forces on the interface as output. During the iterations, a reduced-order model of the flow solver is generated from the inputs and outputs of the solver. The solver that calculates the interface position uses this model to adapt the liquid forces on the gas-liquid interface during the calculation of the interface position.     

A coarse–fine‐mesh stabilization for an alternating Schwarz domain decomposition method

Domain decomposition methods can be solved in various ways. In this paper, domain decomposition in strips is used. It is demonstrated that a special version of the Schwarz alternating iteration method coupled with coarse–fine‐mesh stabilization leads to a very efficient solver, which is easy to implement and has a behavior nearly independent of mesh and problem parameters. The novelty of the method is the use of alternating iterations between odd‐ and even‐numbered subdomains and the replacement of the commonly used coarse‐mesh stabilization method with coarse–fine‐mesh stabilization.     

Mesh and solver co‐adaptation in finite element methods for anisotropic problems

Mesh generation and algebraic solver are two important aspects of the finite element methodology. In this article, we are concerned with the joint adaptation of the anisotropic triangular mesh and the iterative algebraic solver. Using generic numerical examples pertaining to the accurate and efficient finite element solution of some anisotropic problems, we hereby demonstrate that the processes of geometric mesh adaptation and the algebraic solver construction should be adapted simultaneously. We also propose some techniques applicable to the co‐adaptation of both anisotropic meshes and linear solvers. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005     

Discrete boundary smoothing using control node parameterisation for aerodynamic shape optimisation

This paper presents an automated aerodynamic optimisation algorithm using a novel method of parameterising the search domain and geometry by employing user–defined control nodes. The displacement of the control nodes is coupled to the shape boundary movement via a ‘discrete boundary smoothing’. This is initiated by a linear deformation followed by a discrete smoothing step to act on the boundary during the mesh movement based on the change in its second derivative. Implementing the discrete boundary smoothing allows both linear and non-linear shape deformation along the same boundary dependent on the preference of the user. The domain mesh movement is coupled to the shape boundary movement via a Delaunay graph mapping. An optimisation algorithm called Modified Cuckoo Search (MCS) is used acting within the prescribed design space defined by the allowed range of control node displacement. In order to obtain the aerodynamic design fitness a finite volume compressible Navier-Stokes solver is utilized. The resulting coupled algorithm is applied to a range of case studies in two dimensional space including the optimisation of a RAE2822 aerofoil and the optimisation of an intake duct under subsonic, transonic and supersonic flow conditions. The discrete mesh–based optimisation approach outlined is shown to be effective in terms of its generalised applicability, intuitiveness and design space definition.