Robust, broadly applicable fluid-structure interaction (FSI) algorithms remain a challenge for computational mechanics. Efforts in this area are driven by the need to enhance predictive accuracy and efficiency in FSI ...
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Robust, broadly applicable fluid-structure interaction (FSI) algorithms remain a challenge for computational mechanics. Efforts in this area are driven by the need to enhance predictive accuracy and efficiency in FSI simulations, align with experimental observations, and unravel complex multiscale and multiphysics phenomena, while addressing challenges in developing more robust and efficient methodologies. In previous work, we introduced an immersed interface method (IIM) for discrete surfaces and an extension based on an immersed Lagrangia-Eulerian (ILE) coupling strategy for modeling FSI involving complex geometries. The ability of the method to sharply resolve stress discontinuities induced by singular immersed boundary forces in the presence of low-regularity geometrical representations makes it a compelling choice for three-dimensional modeling of complex geometries in diverse engineering applications. Although the IIM we previously introduced offers many desirable advantages, it also imposes a restrictive mesh factor ratio, requiring the surface mesh to be coarser than the fluid grid to ensure stability. This is because when the mesh factor ratio constraint is not satisfied, parts of the structure motion are not controlled by the discrete FSI system. This constraint can significantly increase computational costs, particularly in applications involving multiscale geometries with highly localized complexity or fine-scale features. To address this limitation, we devise a stabilization strategy for the velocity restriction operator inspired by Tikhonov regularization. This study demonstrates that using a stabilized velocity restriction operator in IIM enables a broader range of structure-to-fluid grid-size ratios without compromising accuracy or altering the flow dynamics. This advancement significantly broadens the applicability of the method to real-world FSI problems involving complex geometries and dynamic conditions, offering a robust and computationally effi
In this paper we develop stability and instability criteria for equilibria of nonlinear matrix population models in which density dependence (i.e. nonlinearity) arises through a dependence of vital rates on a weighted...
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In this paper we develop stability and instability criteria for equilibria of nonlinear matrix population models in which density dependence (i.e. nonlinearity) arises through a dependence of vital rates on a weighted total population sizew. These criteria are based upon the net reproductive numbern=n(w) as a function ofwand partially address an earlier conjecture concerning the realtionship between stability and the derivativen=n′(w) (Cushing 1988a). Under rather general conditions it is shown thatn′(w) > 0 at equilibrium implies instability and hence thatn′(w)≤ 0 is necessary for stability. In generaln′(w)< 0 is not sufficient for stability. Conditions under whichn′(w) < 0 does imply stability and also given. A variety of applications is given.
We formulate a thermal-fluid control problem wherein the physics are described by a system of partial differential equations and the control enters through a thermal boundary condition. A finite-element approximation ...
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Thin Si films on SiO2 that are completely melted by pulsed laser irradiation cool rapidly and eventually solidify via nucleation and growth of solids. It has been observed that a variety of solidified microstructures ...
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This paper presents a general formulation of the continuous sensitivity equation method for turbulent heat transfer. The standard k i model of turbulence with wall functions is used to model turbulence. Turbulent heat...
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We present an uncertainty analysis for free convection in corn syrup. One shape-and three valueparameters are considered: height of the enclosure, viscosity and conductivity of corn syrup, and the temperature applied ...
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In this paper we consider the problem of computing optimal feedback control laws for systems of partial differential equations. The problem is motivated by fluid flow control and focuses on computational challenges th...
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A definition of an aircraft agility vector is given and the details for evaluating it are presented. This vector, which represents the time-rate of change of the forces acting on the aircraft, can be given in the usua...
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In this paper, we present some examples of sensitivity analysis for flows modeled by the standard κ - ∈ model of turbulence with wall functions. The flow and continuous sensitivity equations are solved using an adap...
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We are in the process of developing a new laser annealing method referred to as Spot-Beam Crystallization (SBC). The SBC method, which is potentially well suited for manufacturing advanced ultra-high-resolution AMOLED...
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