A new technique for the time-accurate numerical simulation of Euler flows around moving and deforming bodies in 2-D is presented. The grid used is of the stationary, Cartesian, unstructured, Quadtree-based type. The use of a stationary grid is made possible by allowing bodies to move across grid-lines. Use is made of the property that the cells in the immediate vicinity of a moving or stationary body can always be merged together to form combined cells that are topologically invariant over a motion step. Without degrading the global order of accuracy, this merging eliminates the CFL number constraint imposed by cut cells of small area, and eliminates the need for special handling of cells that, due to the motion of bodies across grid-lines, are uncovered or swept-over. The flow solver used is based on a finite-volume conservative formulation, and Roe's approximate-Riemann-solver is used for the computation of interface fluxes. 1-exact spatial reconstruction is used in conjunction with a predictor-corrector explicit timemarching scheme to obtain spatial and temporal second-order accuracies. Gradient limiting is used to enforce monotonicitypreservation near discontinuit,ies. In order to resolve flow features economically and controllably the grid is adaptable to both the geometry and and the flow solution. The computational resources required by this technique are shown to be typical of unstructured-grid implementations. Two computations are presented to demonstrate the capabilities and validity of the technique.
The flow characteristics of a number of underfills were evaluated with quartz dies of different patterns and pitches bonded on different substrate surfaces. Perimeter, mixed array, and full array patterns were tested. Observations on the flow front uniformity, streaking, voiding, and filler segregation were collected. The information was compared with the results predicted by a new simulation code, plastic integrated circuit encapsulationcomputer aided design (PLICE-CAD) under DARPA-funded development. The two-phase model of the combined resin and air takes into account geometrical factors such as bumps and die edges, together with boundary conditions in order to track accurately the propagation of the flow fronts. The two-phase flow field is based on the volume-of-fluid (VOF) methodology embedded in a general-purpose three-dimensional (3-D) flow solver. Index Terms-Capillary flow, filler settling, flip chip, flow simulation, flow streaking, full array pattern, mixed array pattern, organic laminates, peripheral pattern, quartz dies, underfill flow.
This paper presents, discusses, and compares results from experimental and computational studies of the plastic encapsulation process for a 144-lead TQFP package. The experimental results were obtained using an instrumented molding press, while the computational predictions were obtained using a newly-developed software for modeling transfer molding processes. Validation of the software is emphasized, and this was done mainly by comparing the computational results with the corresponding experimental measurements for pressure, temperature, and flow front advancement in the cavities and runners. The experimental and computational results were found to be in good agreement, especially for the flow-front shapes and locations. [S1043-7398(00)00502-8]
We describe our progress toward the development of a unified flow solver (UFS) that can automatically separate nonequilibrium and near-equilibrium domains and switch between continuum and kinetic solvers to combine the efficiency of continuum models with the accuracy of kinetic models. Direct numerical solution of the Boltzmann transport equation is used in kinetic regions, whereas kinetic schemes of gas dynamics are used elsewhere. The efficiency and numerical stability of the UFS is attained by using similar computational techniques for the kinetic and continuum solvers and by employing intelligent domain decomposition algorithms. Different criteria for identifying kinetic and continuum areas and two different mechanisms of coupling Boltzmann and Euler solvers are explored. Solutions of test problems with small Knudsen number are presented to illustrate the capabilities of the UFS for different conditions. It is shown that the UFS can automatically introduce and remove kinetic patches to maximize the accuracy and efficiency of simulations. To our knowledge, this is the first attempt to use direct Boltzmann and continuum flow solvers for developing a hybrid code with solution adaptive domain decomposition.
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