A Multiscale Thermo-Fluid Computational Model for a Two-Phase Cooling System

In this paper, we describe a mathematical model and a numerical simulation method for the condenser component of a novel two-phase thermosyphon cooling system for power electronics applications. The condenser consists of a set of roll-bonded vertically mounted fins among which air flows by either natural or forced convection. In order to deepen the understanding of the mechanisms that determine the performance of the condenser and to facilitate the further optimization of its industrial design, a multiscale approach is developed to reduce as much as possible the complexity of the simulation code while maintaining reasonable predictive accuracy. To this end, heat diffusion in the fins and its convective transport in air are modeled as 2D processes while the flow of the two-phase coolant within the fins is modeled as a 1D network of pipes. For the numerical solution of the resulting equations, a Dual Mixed-Finite Volume scheme with Exponential Fitting stabilization is used for 2D heat diffusion and convection while a Primal Mixed Finite Element discretization method with upwind stabilization is used for the 1D coolant flow. The mathematical model and the numerical method are validated through extensive simulations of realistic device structures which prove to be in excellent agreement with available experimental data

Numerical results for mimetic discretization of Reissner-Mindlin plate problems

A low-order mimetic finite difference (MFD) method for Reissner-Mindlin plate problems is considered. Together with the source problem, the free vibration and the buckling problems are investigated. Full details about the scheme implementation are provided, and the numerical results on several different types of meshes are reported

Adaptive Mesh Refinement Computation of Solidification Microstructures using Dynamic Data Structures

We study the evolution of solidification microstructures using a phase-field model computed on an adaptive, finite element grid. We discuss the details of our algorithm and show that it greatly reduces the computational cost of solving the phase-field model at low undercooling. In particular we show that the computational complexity of solving any phase-boundary problem scales with the interface arclength when using an adapting mesh. Moreover, the use of dynamic data structures allows us to simulate system sizes corresponding to experimental conditions, which would otherwise require lattices greater that $2^{17}\times 2^{17}$ elements. We examine the convergence properties of our algorithm. We also present two dimensional, time-dependent calculations of dendritic evolution, with and without surface tension anisotropy. We benchmark our results for dendritic growth with microscopic solvability theory, finding them to be in good agreement with theory for high undercoolings. At low undercooling, however, we obtain higher values of velocity than solvability theory at low undercooling, where transients dominate, in accord with a heuristic criterion which we derive

Blending liquids

We present a method for smoothly blending between existing liquid animations. We introduce a semi-automatic method for matching two existing liquid animations, which we use to create new fluid motion that plausibly interpolates the input. Our contributions include a new space-time non-rigid iterative closest point algorithm that incorporates user guidance, a subsampling technique for efficient registration of meshes with millions of vertices, and a fast surface extraction algorithm that produces 3D triangle meshes from a 4D space-time surface. Our technique can be used to instantly create hundreds of new simulations, or to interactively explore complex parameter spaces. Our method is guaranteed to produce output that does not deviate from the input animations, and it generalizes to multiple dimensions. Because our method runs at interactive rates after the initial precomputation step, it has potential applications in games and training simulations

Numerical Methods for Parasitic Extraction of Advanced Integrated Circuits

FFinFETs, also known as Fin Field Effect Transistors, are a type of non-planar transistors used in the modern integrated circuits. Fast and accurate parasitic capacitance and resistance extraction is crucial in the design and verification of Fin- FET integrated circuits. Though there are wide varieties of techniques available for parasitic extraction, FinFETs still pose tremendous challenges due to the complex geometries and user model of FinFETs. In this thesis, we propose three practical techniques for parasitic extraction of FinFET integrated circuits. The first technique we propose is to solve the dilemma that foundries and IP vendors face to protect the sensitive information which is prerequisite for accurate parasitic extraction. We propose an innovative solution to the challenge, by building a macro model around any region in 2D/3D on a circuit where foundries or IP vendors wish to hide information, yet the macro model allows accurate capacitance extraction inside and outside of the region. The second technique we present is to reduce the truncation error introduced by the traditional Neumann boundary condition. We make a fundamental contribution to the theory of field solvers by proposing a class of absorbing boundary conditions, which when placed on the boundary of the numerical region, will act as if the region extends to infinity. As a result, we can significantly reduce the size of the numerical region, which in turn reduces the run time without sacrificing accuracy. Finally, we improve the accuracy and efficiency of resistance extraction for Fin-FET with non-orthogonal resistivity interface through FVM and IFEM. The performance of FVM is comparable to FEM but with better stability since the conservation law is guaranteed. The IFEM is even better in both efficiency and mesh generation cost than other methods, including FDM, FEM and FVM. The proposed methods are based on rigorous mathematical derivations and verified through experimental results on practical example