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A novel smoothness indicator is proposed herein for WENO schemes based on the point-wise local variation in the candidate stencils. The proposed indicator is further used to define non-linear weights for a WENO scheme. The main feature of the resulting schemes is that they give a higher resolution of the solution compared to other state of art WENO schemes, e.g., WENO-JS, WENO-Z and very recent WENO-L. Moreover, these resulting WENO schemes maintain high-order accuracy and retains the non-oscillatory approximation property. The computational cost of the new scheme is comparable to WENO-Z and WENO-JS schemes. Computational results of selected benchmark test problems illustrate the higher resolution, accuracy and non-oscillatory property of the new schemes. [ABSTRACT FROM AUTHOR]

The stress concentration and deformation of the 3D stacked IC structures can be minimized with an optimal design of the integrated circuit (IC) using a response surface methodology. The geometrical and process parameters (i.e., A = inlet pressure, B = solder bump standoff height, C = chip thickness, and D = aspect ratio) were optimized via a central composite design (CCD) for the molded encapsulation process. The fluid/structure interaction (FSI) aspects were considered in the optimization of the molded encapsulation process. The separate effects of the independent variables and their interactions were studied. The calculated empirical models were carried out and well validated with the simulation results. The optimum geometrical and process parameters of the 3D stacked IC package with perimeter solder bump arrangement were characterized as follows: inlet condition of 3.65 MPa, 150 μm of solder bump standoff height, 250 μm of chip thickness, and 2.1 of aspect ratio. The outcomes herein may significantly contribute to the advancement of microelectronic industries. [ABSTRACT FROM AUTHOR]

An entropy-stable residual distribution (RD) method is developed for the systems of two-dimensional shallow water equations (SWE). The construction of entropy stability for the residual distribution method is derived from finite volume method principles, albeit using a multidimensional approach. The paper delves into in-depth discussions on how finite volume methods achieve entropy stability in a "one-dimensional" sense for two-dimensional systems of SWE unlike the residual distribution methods. Results herein demonstrate the superiority of the entropy-stable RD methods relative to their finite volume counterparts, especially on highly irregular triangular grids. The comparative results with other established RD methods are also included, depicting similar performances with the Lax–Wendroff method for unsteady smooth flows but more accurate than the multidimensional upwind approaches (N, LDA) on both smooth and discontinuous test cases. [ABSTRACT FROM AUTHOR]

This study investigates the effects of filling level and fillet profile on a solder joint strength between pin-through hole (PTH) and a printed circuit board. The influences of filling level and fillet profile on deformation, von Mises stress and strain are the focus of this research. Five filling levels (20%, 40%, 60%, 80% and 100%) and fillet profiles (0.2, 0.4, 0.6, 0.8 and 1.0) are considered. The Abaqus software is used to examine the PTH structure. A tension test experiment is conducted on a single PTH connector, and its results are compared with the simulation results. The simulation and experimental results show an almost identical linear trend with an average discrepancy of 3.39%. Results show that an increase in the filling level and the fillet profile increases the structural deformation/displacement and the von Mises stress. The displacement and the von Mises stress of the PTH exhibit a linear correlation with the filling level and the fillet profile. This study is expected to provide a good understanding of solder joint strength during wave soldering. [ABSTRACT FROM AUTHOR]

This paper solves the advection-diffusion equation by treating both advection and diffusion residuals in a separate (non-unified) manner. An alternative residual distribution (RD) method combined with the Galerkin method is proposed to solve the advection-diffusion problem. This Flux-Difference RD method maintains a compact-stencil and the whole process of solving advection-diffusion does not require additional equations to be solved. A general mathematical analysis reveals that the new RD method is linearity preserving on arbitrary grids for the steady-state advection-diffusion equation. The numerical results show that the flux difference RD method preserves second-order accuracy on various unstructured grids including highly randomized anisotropic grids on both the linear and nonlinear scalar advection-diffusion cases. [ABSTRACT FROM AUTHOR]

In this paper, the properties of the newly developed flux-difference residual distribution methods will be analyzed. The focus would be on the order-of-accuracy and stability variations with respect to changes in grid skewness. Overall, the accuracy loss and the stability range of the new methods are comparable with the existing residual distribution methods. It will also be shown that new method has a general mathematical formulation which can easily recover the existing residual distribution methods. [ABSTRACT FROM AUTHOR]

Even though the mechanical heart valve (MHV) has been used routinely in clinical practice for over 60 years, the occurrence of serious complications such as blood clotting remains to be elucidated. This paper reviews the progress that has been made over the years in terms of numerical simulation method and the contribution of abnormal flow toward blood clotting from MHVs in the aortic position. It is believed that this review would likely be of interest to some readers in various disciplines, such as engineers, scientists, mathematicians and surgeons, to understand the phenomenon of blood clotting in MHVs through computational fluid dynamics. [ABSTRACT FROM AUTHOR]

This paper presents an analytical and numerical approach in studying accuracy deterioration of residual distribution and cell-vertex finite volume methods on triangular grids. Results herein demonstrate that both methods preserve the order-of-accuracy reasonably well for uniformly skewed triangular grids and the $$L_2$$ errors of both second-order accurate methods behave similarly with values of the same magnitude. On the other hand, the first-order finite volume method has an $$L_2$$ error of about an order of magnitude higher than its residual distribution counterpart. Both first-order methods are unable to preserve the order-of-accuracy for high-frequency data when the grids are highly skewed although the residual distribution approach has a slightly better performance. Both second-order methods perform quite decently for high-frequency data on uniformly skewed grids. However, the order-of-accuracy of finite volume methods excessively deteriorate when the grids are skewed non-uniformly unlike the residual distribution methods which preserve the order-of-accuracy. [ABSTRACT FROM AUTHOR]

The performance of the classic upwind-type residual distribution (RD) methods on skewed triangular grids are rigorously investigated in this paper. Based on an improved signals distribution, an improved second order RD method based on the LDA approach is proposed to faithfully replicate the flow physics on skewed triangular grids. It will be mathematically and numerically shown that the improved LDA method is found to have minimal accuracy variations when grids are skewed compared to classic RD and cell vertex finite volume methods on scalar equations and system of Euler equations. [ABSTRACT FROM AUTHOR]

Unsteady Reynolds averaged Navier-Stokes (URANS) computations of standard maneuvers are performed for a surface combatant at model and full scale. The computations are performed using CFDShip-Iowa v4, a free surface solver designed for 6DOF motions in free and semi-captive problems. Overset grids and a hierarchy of bodies allow the deflection of the rudders while the ship undergoes 6DOF motions. Two types of maneuvers are simulated: steady turn and zigzag. Simulations of steady turn at 35° rudder deflection and zigzag 20/20 maneuvers for Fr = 0.25 and 0.41 using constant RPM propulsion are benchmarked against experimental time histories of yaw, yaw rate and roll, and trajectories, and also compared against available integral variables. Differences between CFD and experiments are mostly within 10 % for both maneuvers, highly satisfactory given the degree of complexity of these computations. Simulations are performed also with waves, and with propulsion at either constant RPM or torque. 20/20 zigzag maneuvers are simulated at model and full scale for Fr = 0.41. The full scale case produces a thinner boundary layer profile compared to the model scale with different reaction times and handling needed for maneuvering. Results indicate that URANS computations of maneuvers are feasible, though issues regarding adequate modeling of propellers remain to be solved. [ABSTRACT FROM AUTHOR]

In this paper, a study on limited Rotated Richtmyer scheme is performed with a focus on vorticity prediction. It will be mathematically and numerically demonstrated that the Rotated Richtmyer scheme coupled with a TVD limiter can retain both irrotational and rotational flow when solving pure acoustics equations. However, the limited Rotated Richtmyer scheme cannot preserve irrotational flow if the advection terms are included. [ABSTRACT FROM AUTHOR]