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Microchannel is helpful for cooling the microelectronic devices with high heat flux. In this study, topology optimization method with three objective functions (pumping power, bottom wall mean temperature and temperature uniformity) is adopted to optimize the structure of a manifold microchannel. The field synergy principle is used to evaluate the optimized structures. Several single-objective, bi-objective, and triple-objective function problems are numerically studied. It is found that the obtained structures with better cooling performance always present low synergy angle, in consistent with the field synergy principle. The optimized structures perform better than conventional microchannel with ribs. Effects of inlet velocity, thermal diffusivity ratio and heat flux at the bottom wall are also investigated. The topology optimization method with triple-objective functions is effective to improve the performance of manifold microchannels. [ABSTRACT FROM AUTHOR]

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 replace a unit operator (first level) and an orthogonal project operator (second level). The present VMS-MLPG method allows arbitrary combinations of interpolation functions for the velocity and pressure fields, specifically the equal-order interpolations that are easy to implement and satisfy the Babuska-Breezi (B-B) condition. The prediction accuracy and the numerical stability of the proposed method for the lid-driven cavity flow and the backward facing step flow problems are analyzed and validated by comparing with the SUMLPG method and the benchmark solutions. It is shown that the present VMS-MLPG method can guarantee the numerical stability and obtain the reasonable solutions for incompressible Navier-Stokes equation. [ABSTRACT FROM AUTHOR]

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 convergence. So far, there is not any doable applied method to determine the best relaxation factor of SUR. In this article, the interrelation among the diffusion term, the convection term and the under-relaxation term is regarded as the key to calculate the under-relaxation factor. Then, the self-adaptive under-relaxation factor strategy is proposed. The test calculation of two typical problems, lid-driven cavity flow, and flow over a backward-facing step is carried out based on the proposed self-adaptive under-relaxation strategy. It is proved that the present method is efficient and robust compared to the fixed under-relaxation factor method. [ABSTRACT FROM AUTHOR]

The numerical oscillation will occur in convection-diffusion equations as special linear problems at large Peclet number (Pe) in the numerical calculation process. In this article, we propose a new definition of the stability parameter in streamline upwind meshless Petrov-Galerkin (SUMLPG) method. The most important feature of the proposed method is that the test function in the stabilization term is taken into the differential operator-like form The stability parameter is designed to adjust the convection strength to achieve accurate and stable numerical solutions. Several classical examples are adopted to assessment the accuracy and stability of the proposed stability parameter. It is proven that the proposed method is especially suitable for convection-diffusion problems with large Pe. [ABSTRACT FROM AUTHOR]

In some pressure-based methods, inner iteration processes are introduced to achieve efficient solutions. However, number of the inner iteration is fixed as 2 or 4 for different computations. In this paper, a mechanism is proposed to control inner iteration processes to make the number of inner iterations vary adaptively with different problems. The adaptive inner iteration processes are used in viscous compressible flows. Results reveal that by introducing inner iteration processes, computational efficiency is highly improved compared with that of the solution without inner iteration. In addition, adaptive inner iteration solutions have better robustness than fixed inner iteration solutions. [ABSTRACT FROM AUTHOR]

A hybrid flux splitting scheme, called AUSM+–FVS((advection upstream splitting method)+–flux vector splitting), is proposed in this article to calculate the inviscid fluxes of Euler/Navier–Stokes equations. This new scheme is obtained by hybridizing the AUSM+ scheme with FVS method. When the local Mach number tends to zero, this scheme is similar to the AUSM+. Contrarily, this scheme is similar to the FVS at the shock region. Thus, this scheme has the accuracy of AUSM+ in boundary layer region and the robustness of FVS in shock region. Several numerical tests show that AUSM+–FVS can reduce the shock instability and has a good accuracy in boundary layer region. [ABSTRACT FROM PUBLISHER]

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 convection-dominated problems. In the present VMS-SUMLPG method, the streamline upwind is constructed in the test function to solve the non-self-adjoint matrix. Meanwhile, the VMS concept as a stability term is adopted to alleviate the numerical instability such as spurious oscillations, overshoots, and undershoots. Its numerical accuracy and stability are validated by comparing with the streamline upwind Petrov–Galerkin (SUMLPG) method and the finite volume method with high-order difference schemes for two classical convection-dominated problems at the Peclet number ranging from 106to 108. It is shown that the numerical solutions of the present VMS-SUMLPG method are accuracy, smoothness, and stability. [ABSTRACT FROM PUBLISHER]

The effect of round-off errors on the solution of numerical heat transfer is illustrated by a simple example both analytically and numerically. It is found that the upper bound of the round-off error under both conditions with or without an inner heat source is proportional to the square of grid number—n2. Increase in grid number might lead to larger round-off errors. The magnitude of relative round-off error is also determined by the specific problem. Proper treatment of the computation procedure can reduce the round-off error obviously. The precision can be improved with this method without occupation of additional computational resources. [ABSTRACT FROM PUBLISHER]

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. [ABSTRACT FROM AUTHOR]

Anisotropy problems are widely encountered in practical applications. In the present paper, a parallel and scalable multigrid (MG) method combined with the high-order compact difference scheme is employed to solve an anisotropy model equation on a rectangular domain. The present method is compared with the MG combined with the standard central difference scheme. Numerical results show that the MG method combined with the high-order compact difference scheme is more accurate and efficient than the MG with the standard central difference scheme for solving anisotropy elliptic problems. MG components (restriction, prolongation, relaxation, and cycling) and the corresponding parallelism characteristics are also discussed. [ABSTRACT FROM AUTHOR]

A new hybrid algorithm based on the lattice Boltzmann method (LBM) and the finite-volume method (FVM) is proposed for numerically calculating the emissions of volatile organic compounds (VOCs) from building materials and predicting their space distribution. Most building envelopes are comprised of single as well as multilayer materials, with some of them being porous and others nonporous. First, only the LBM is used to calculate the VOC concentration in airtight and ventilated chambers with constant as well as variable ventilation. For multilayer materials, including both porous and nonporous, half-lattice division methodology in the LBM is used, which ensures flux continuity at the interfaces. Good agreement is found between computed results and experimental data available in the literature. The effect of variable ventilation is also studied for both types of sequences of porous/nonporous layers. Then the LBM coupled with the FVM is used to investigate the VOC concentration distribution in the room emitted from styrene-butadiene rubber (SBR) plate, and good agreement is found between obtained results and those already published. The hybrid algorithm with multilayer approach is also used to conduct a detailed study of the effect of different ventilation organizations on the concentration in the room air, and the best one is found by the simulation. [ABSTRACT FROM AUTHOR]

A fully compressible multispeed lattice Boltzmann model is introduced and numerically demonstrated to simulate compressible thermal flow. The equilibrium distribution functions are derived by a nonperturbative algebraic theory in coordinate symmetry product form to avoid complex polynomial expansion of the Maxwellian function and Gauss-Hermite quadrature. An important characteristic of the proposed model is that it can be easily extendied to a multidimentional model with factorization symmetry. For compressible flows, Sod shock tube, Couette flow, and high-Mach double-reflection compressible flow are carried out to validate the present model for compressible flow and heat transfer. Numerical results are in excellent agreement with the theoretical solutions of fluid flows. [ABSTRACT FROM AUTHOR]

In this article, a comparison is made between the robustness and efficiency of the CLEAR algorithm and the SIMPLE algorithm on nonorthogonal curvilinear coordinates for compressible flows. Thirteen different high-order convection schemes are employed in the calculations. Subsonic flow, transsonic flow, and supersonic flow in a channel with a circular arc bump and compressible flow in a Laval nozzle are used as test cases. The CLEAR algorithm shows huge potential to compute the transsonic flow in the Laval nozzle and high-speed compressible flows. Results with the ADBQUICKEST scheme, the HLPA scheme, and the MUSCL scheme are stable for both the compressible SIMPLE and CLEAR algorithms for all the mentioned cases. [ABSTRACT FROM AUTHOR]

In this article, comparative studies on computational accuracies and convergence rates of triangular and quadrilateral meshes are carried out in the frame work of the finite-volume method. By theoretical analysis, we conclude that the number of triangular cells needs to be 4/3 times that of quadrilateral cells to obtain similar accuracy. The conclusion is verified by a number of numerical examples. In addition, the convergence rates of the triangular meshes are found to be slower than those of the quadrilateral meshes when the same accuracy is obtained with these two mesh types. [ABSTRACT FROM AUTHOR]

It is well known that convection-diffusion equations suffer from the most difficult problems to gain a stable and accurate solution. Sometimes, the convection terms may cause oscillatory behavior of solutions. In this article, the streamline upwind Petrov-Galerkin (SUPG) scheme is applied to eliminate overshoots and undershoots produced by the convection term in the meshless local Petrov-Galerkin (MLPG) method. The accuracy and stability of the present method are discussed using two test cases. The results of the present method are compared with results of other upwind schemes and the finite volume method (FVM) using a high-order upwind scheme. Our analysis shows that the present method, with its simple implementation, can give excellent results for convection-dominated problems. [ABSTRACT FROM PUBLISHER]

Recently an efficient segregated algorithm for incompressible fluid flow and heat transfer problems, called IDEAL (Inner Doubly Iterative Efficient Algorithm for Linked Equations), has been proposed by the present authors. In the algorithm there exist inner doubly iterative processes for the pressure equation at each iteration level, which almost completely overcome the two approximations in the SIMPLE algorithm. Thus the coupling between velocity and pressure is fully guaranteed, greatly enhancing the convergence rate and stability of the solution process. In this article, the IDEAL algorithm is extended to the body-fitted collocated grid systems in 3-D nonorthogonal curvilinear coordinates. The extended IDEAL algorithm adopts two successful methods. One is that the interfacial contravariant velocity is calculated by the modified momentum interpolation method (MMIM); the other is that the interfacial contravariant velocity is improved by solving the pressure equation directly. Finally, three 3-D incompressible fluid flow and heat transfer problems are provided to compare the convergence rate and robustness between IDEAL and three other algorithms (SIMPLEM, SIMPLERM, and SIMPLECM). From the comparison it can be concluded that the IDEAL algorithm is more robust and efficient than the three other algorithms. [ABSTRACT FROM AUTHOR]

Discussions are given of the different momentum interpolation methods to evaluate the interface velocity in the collocated grid system. It is pointed out that the interface velocity is used in three cases in the overall numerical procedure of the solution of Navier-Stokes equations by utilizing a collocated grid: in the continuity equation; in the interface flow rate computation for the determination of the coefficients in discretization equation; and in the mass residual in the coefficient Ap. Analysis shows that it is better to adopt the momentum interpolation method in the three cases. Two new momentum interpolation methods, called MMIM1 and MMIM2, are proposed. Analysis shows that the two new methods can achieve numerical solutions that are independent of both the underrelaxation factor and the time step size. Taking lid-driven cavity flow as an example, numerical computations are conducted for several Reynolds numbers and different mesh sizes using the SIMPLE algorithm, and the results are compared with benchmark solutions. Numerical tests demonstrate that both MMIM1 and MMIM2 can give unique solutions for different underrelaxation factors and time step sizes, solutions from MMIM1 are slightly better than that of the momentum interpolation of Majumdar, and solutions from MMIM2 have an appreciably better accuracy when the mesh is not fine. [ABSTRACT FROM AUTHOR]

Provides numerical cases of the undesirable features inherent in the original momentum interpolation. Factors affecting checkerboard pressure predictions; Disadvantage of the usage of the original R hie and Chow interpolation; Effect of time step size on the converged solution.

A new method is proposed to accelerate the convergence rate for the SIMPLER algorithm by artificially changing the underrelaxation term to match the dependent variable to be solved. Based on this idea, a new pressure-correction equation is derived, and the modified algorithm is named MSIMPLER. Five numerical experiments show that the MSIMPLER algorithm can appreciably enhance the convergence rate for cases of low and moderate underrelaxation factors with good robustness. [ABSTRACT FROM AUTHOR]

A comprehensive study is presented regarding the numerical stability of several common iteration numerical methods applied to the discretized steady convective-diffusion equations with some common finite-difference spatial discretizations. One-dimensional and multidimensional results are obtained using the classical Von Neumann method of stability analysis. The analysis results show that numerical stability in solving the resulting discretization equations depends on both the finite-difference scheme and the numerical method for solving the resulting algebraic equations. [ABSTRACT FROM AUTHOR]