operator splitting algorithms are frequently used for solving the advection-diffusion equation, especially to deal with advection dominated transport problems. In this paper an operator splitting algorithm for the thr...
详细信息
operator splitting algorithms are frequently used for solving the advection-diffusion equation, especially to deal with advection dominated transport problems. In this paper an operator splitting algorithm for the three-dimensional advection-diffusion equation is presented. The algorithm represents a second-order-accurate adaptation of the Holly and Preissmann scheme for three-dimensional problems. The governing equation is split into an advection equation and a diffusion equation, and they are solved by a backward method of characteristics and a finite element method, respectively. The Hermite interpolation function is used for interpolation of concentration in the advection step. The spatial gradients of concentration in the Hermite interpolation are obtained by solving equations for concentration gradients in the advection step. To make the composite algorithm efficient, only three equations for first-order concentration derivatives are solved in the diffusion step of computation. The higher-order spatial concentration gradients, necessary to advance the solution in a computational cycle, are obtained by numerical differentiations based on the available information. The simulation characteristics and accuracy of the proposed algorithm are demonstrated by several advection dominated transport problems. (C) 1998 John Wiley & Sons, Ltd.
The present study considers transient buoyancy-opposed double diffusive free convection of a micropolar fluid consisting of rigid and non-deformable particles suspension with its own rotation in a square enclosure. Th...
详细信息
The present study considers transient buoyancy-opposed double diffusive free convection of a micropolar fluid consisting of rigid and non-deformable particles suspension with its own rotation in a square enclosure. The governing equations are written in terms of the primitive variables and a numerical solution of the complete set of nonlinear equations has been done without any scaling to the flow terms. The modified Market and Cell (MAC) method is used for the solution of the variables in the primitive form with the help of the Alternating Direction Implicit (ADI) scheme. In order to handle effectively the advection terms, the gradient dependent consistent hybrid upwind scheme of second order (GDCHUSSO) and the operator-splittingalgorithm have been employed. A parametric study is conducted to illustrate the effects of the Rayleigh number, Prandtl number, buoyancy ratio and the vortex viscosity parameter. Interesting features of stability at critical buoyancy ratios with the inclusion of the vortex viscosity parameter is reported. Detailed distributions of isotherms, isoconcentrations, flow lines and microrotation lines are provided to reveal the concealed physics of the complex phenomenon. A power spectrum analysis and phase plane maps are provided to bring clarity about the instability involved in the phenomenon. Correlations have been developed for the average Nusselt and Sherwood numbers based on the computed results. (C) 2014 Elsevier Ltd. All rights reserved.
The present work deals with magnetoconvection of molten gallium in a cuboid rotating about a vertical axis passing through its center. The governing equations are derived in a non-inertial frame of reference consideri...
详细信息
The present work deals with magnetoconvection of molten gallium in a cuboid rotating about a vertical axis passing through its center. The governing equations are derived in a non-inertial frame of reference considering both centrifugal and Coriolis forces. A vertical magnetic field is applied through the center opposite to the direction of gravity. The cuboid is heated from below and cooled at top, while the remaining walls of the cuboid are thermally insulated. The modified Marker and Cell method is adopted for the numerical solution of the governing equations. The gradient dependent consistent hybrid upwinding scheme of second order is adopted for the discretization of the convective terms in the momentum equations. The operator splitting algorithm is used for the numerical treatment of the energy equation. The effects of cavity rotation and applied magnetic field on heat and momentum transport processes have been investigated. The uniform thorough mixing of fluids by rotation and regularization of flow by magnetic field are observed. The governing flow field and temperature distribution are shown graphically to elucidate the intricate physics of the phenomenon. (C) 2014 Elsevier Ltd. All rights reserved.
The present analysis reports interesting results regarding the effect of surface radiation on the transient behavior of mixed convection in a bottom-heated cavity having gray and diffuse walls. Movement of the walls c...
详细信息
The present analysis reports interesting results regarding the effect of surface radiation on the transient behavior of mixed convection in a bottom-heated cavity having gray and diffuse walls. Movement of the walls causes shear-induced flow within the cavity, which either augments or attenuates the buoyancy-induced flow and results mixed convection. The effect of various influencing parameters such as the Rayleigh number (Ra), Richardson number (Ri), wall movement direction, and emissivity of the walls (epsilon) on the flow and heat transfer characteristics has been analyzed. Weak conservative form of governing equations are solved using the modified Marker and Cell method. A gradient-dependent consistent hybrid upwind scheme of the second order is used for discretization of the convective terms in the flow equation. An operator splitting algorithm is used to solve the energy equation. The surface radiation transport equation has been solved using the net radiation method. It is noticed from the present analysis that the dominance of shear-induced flow is more compared to buoyancy-induced flow in the case of horizontal wall movement. The time required to attain steady state is more for vertical wall movement in mixed convection regimes. The oscillating behavior of the average heat transfer with time;increases with the increase in the Rayleigh number and emissivity. Unicellular and multi-cellular flow structures are observed depending on the type of wall movement and other controlling parameters.
We present a robust method to infer network topology in the presence of outliers from given observations at nodes under the structural equation model. We introduce auxiliary matrices modeling Gaussian noise and sparse...
详细信息
ISBN:
(纸本)9798350372267;9798350372250
We present a robust method to infer network topology in the presence of outliers from given observations at nodes under the structural equation model. We introduce auxiliary matrices modeling Gaussian noise and sparse outliers. The topology identification task is cast as a minimization problem of the sum of three terms under constraints involving a bilinear form: (i) the squared Frobenius norm of the noise matrix, (ii) the l(1) norm of the adjacency matrix, and (iii) a weakly-convex sparsity-promoting function (the minimax concave penalty) of the outlier matrix. The problem is reformulated into an unconstrained optimization problem by introducing a linear operator, and an efficient alternating minimization method is presented. Simulation results show remarkable robustness of the proposed method.
The EMI model represents excitable cells in a more accurate manner than traditional homogenized models at the price of increased computational complexity. The increased complexity of solving the EMI model stems from a...
详细信息
The EMI model represents excitable cells in a more accurate manner than traditional homogenized models at the price of increased computational complexity. The increased complexity of solving the EMI model stems from a significant increase in the number of computational nodes and from the form of the linear systems that need to be solved. Here, we will show that the latter problem can be solved by careful use of operatorsplitting of the spatially coupled equations. By using this method, the linear systems can be broken into sub-problems that are of the classical type of linear, elliptic boundary value problems. Therefore, the vast collection of methods for solving linear, elliptic partial differential equations can be used. We demonstrate that this enables us to solve the systems using shared-memory parallel computers. The computing time scales perfectly with the number of physical cells. For a collection of 512 x 256 cells, we solved linear systems with about 2.5 x 10(8) unknows. Since the computational effort scales linearly with the number of physical cells, we believe that larger computers can be used to simulate millions of excitable cells and thus allow careful analysis of physiological systems of great importance.
暂无评论