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A two-level variational multiscale meshless local Petrov-Galerkin (VMS-MLPG) method is presented for incompressible Navier-Stokes equations based on two local Gauss integrations which effectively r...

The method of successive under-relaxation (SUR) is an effective way for numerically solving a nonlinear system of equations governing the fluid flow and heat transfer, resulting in stable convergen...

A meshless local Petrov–Galerkin (MLPG) approach based on the streamline upwind (SU) idea and the variational multiscale (VMS) concept, called as VMS-SUMLPG method, is herein proposed to solve the ...

A physically consistent difference scheme is proposed to discretize the convection–diffusion equation in this paper. The interface variables of control volume are calculated by the interpolation of the discretized convection–diffusion equation rather than the direct interpolation with neighbor nodes in the direction perpendicular to the interface. In the new scheme, all the nodes of parallel and normal to the interface are involved, which means that the influence of cross-stream fluxes is considered. Obviously, the proposed interpolation scheme is full of physical meaning and better than the traditional convective interpolation schemes. Two simulations of typical benchmark problems, lid-driven cavity flow in square cavity and flow over a backward-facing step, are carried out with this scheme and some traditional schemes to prove the advantages of the proposed scheme.

This article presents a 2-D numerical simulation on nucleate boiling using the VOSET method. Heat transfer through a liquid microlayer around a three-phase contact point is incorporated by a multiscale system method. A temperature interpolation method is presented for solving temperature field in cells containing liquid-vapor interface. Apart from the single-bubble model, computations are carried out for two-bubble and bubble merger models. Heat fluxes predicted by simulation are compared with experimental correlations and good agreement is obtained. In addition, simulation results of bubble's behavior also verify some boiling mechanisms.

In the companion article (Part I), simplified compact model of components in a system level model was established based on heat transfer path and thermal resistance network analysis. In this article, component level simulation and lead level simulation was conducted by assiging the boundary conditions from the data of the higher level simulation, and effects of different boundary conditions on numerical accuracy and stability are studied. Comparison shows that multiscale thermal modeling methodology can save 87% of the total computation time compared with full simulation with a fine grid system, and can greatly improve the resolution of the calculation result. Mainly based on the multiscale simulation five improvements for the reduction of the maximum PCB temperature are proposed. This article also provides an example that by a careful numerical thermal design, a passive cooling mode can sometimes meet the cooling requirement of a PCB with high power input in some extent.

Passive cooling schemes, such as natural convection, are the most reliable heat dissipation apprpaches for electronic equipment. Some times, the highest temperature of the printed circuit board (PCB), rather than the highest of chips, is very much concern because of some technological reasons. In order to reduce the maximum PCB temperature, this article analyze the PCB temperature distribution by multiscale simulation. A top-to-down approach is adopted in order to reveal the details of temperature distribution of some interested local position. In the top-to-down approach, the system level simulation by a not-too-fine grid system is the key to obtain a reliable solution. In order to reach such a goal each component of the PCB should be reasonably simplified. The thermal analysis method is proposed to simplify the components, and the implementation details are provided for three types of components. In the companion article, the settlement of boundary conditions from the data of system level simulation and...

The inconsistency of the second hypothesis of the SIMPLE-like algorithms is analyzed and a remedy—the Consistent Update Technique (CUT algorithm)—for velocity and pressure is proposed. In the CUT algorithm, at each iterative level the mass conservation condition is satisfied implicitly while the momentum equation is satisfied explicitly. In CUT algorithm, a modified equation for the explicit-velocity is suggested, and an adjustable coefficient is introduced. Four 2-D fluid flow and heat transfer problems are solved numerically by both the CUT and SIMPLER algorithms under the same other conditions. Comparisons of CPU time are made and it is found that for the four examples studied, the CUT can at least reduce CPU time by 15–63% with much better robustness.

For periodic fully developed fluid flow and heat transfer problems, it is sufficient to confine attention to a single cycle. The temperature periodic conditions at the computational domain inlet/exit for fluid temperature can be implemented by two methods: either by extending the computational domain by several control volumes and replacing the field data at the domain inlet and outlet by each other, or by using linear interpolation while restricting the computation within one module. By carefully examining the numerical solutions of the fluid streamwise bulk temperature obtained from the two methods, it is found that at the fluid bulk temperature varies abruptly at the domain exit. A comprehensive analysis reveals that this abnormal phenomenon is caused by the fact that the domain exit fluid bulk temperature is actually not updated with iteration. A remedy is proposed: The domain exit bulk temperature is updated by an upwind-based interpolation method. Numerical examples show that the second-order interp...

Based on the stability-controllable second-order difference (SCSD) scheme, a new stability-guaranteed second-order difference (SGSD) scheme is proposed whose merits are absolutely stable and adaptive. Its numerical accuracy is at least no less than that of the central difference (CD) and second-order upwind difference (SUD) schemes and sometimes higher than that of the QUICK scheme. The SGSD scheme can automatically choose a different difference scheme according to the available local field information in difference space or time. It automatically approaches the central difference scheme where or when diffusion is dominant, and approaches the second-order upwind difference scheme where or when convection is dominant. Computations for two benchmark problems using the SGSD and the other three schemes show its feasibility in engineering computations.