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Cubic Elements (cubic + element)
Selected AbstractsPrediction of thermal sensation based on simulation of temperature distribution in a vehicle cabinHEAT TRANSFER - ASIAN RESEARCH (FORMERLY HEAT TRANSFER-JAPANESE RESEARCH), Issue 3 2001Takuya Kataoka Abstract Thermal comfort in an automobile is predicted with numerical simulation. The flow field and temperature distribution are solved with a grid system based on many small cubic elements which are generated automatically with cabin and passenger configuration. Simulation of temperature is combined with simulation of cooling cycle and calculation of heat transfer at the wall including solar radiation to treat transient and actual driving conditions of the vehicle. In order to evaluate thermal comfort, transitional effective temperature is calculated from simulated thermal conditions and physiologic values which are calculated by a simple model of a human thermal system. This system can well predict thermal sensation of passengers in a short period of time. © 2001 Scripta Technica, Heat Trans Asian Res, 30(3): 195,212, 2001 [source] Optimal stress recovery points for higher-order bar elements by Prathap's best-fit methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 8 2009S. Rajendran Abstract Barlow was the first to propose a method to predict optimal stress recovery points in finite elements (FEs). Prathap proposed an alternative method that is based on the variational principle. The optimal points predicted by Prathap, called Prathap points in this paper, have been reported in the literature for linear, quadratic and cubic elements. Prathap points turn out to be the same as Barlow points for linear and quadratic bar elements but different for cubic bar element. Nevertheless, for all the three elements, Prathap points coincide with the reduced Gaussian integration points. In this paper, an alternative implementation of Prathap's best-fit method is used to compute Prathap points for higher-order (viz., 4,10th order) bar elements. The effectiveness of Prathap points as points of accurate stress recovery is verified by actual FE analysis for typical bar problems. Copyright © 2008 John Wiley & Sons, Ltd. [source] A variational multiscale model for the advection,diffusion,reaction equationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 7 2009Guillaume Houzeaux Abstract The variational multiscale (VMS) method sets a general framework for stabilization methods. By splitting the exact solution into coarse (grid) and fine (subgrid) scales, one can obtain a system of two equations for these unknowns. The grid scale equation is solved using the Galerkin method and contains an additional term involving the subgrid scale. At this stage, several options are usually considered to deal with the subgrid scale equation: this includes the choice of the space where the subgrid scale would be defined as well as the simplifications leading to compute the subgrid scale analytically or numerically. The present study proposes to develop a two-scale variational method for the advection,diffusion,reaction equation. On the one hand, a family of weak forms are obtained by integrating by parts a fraction of the advection term. On the other hand, the solution of the subgrid scale equation is found using the following. First, a two-scale variational method is applied to the one-dimensional problem. Then, a series of approximations are assumed to solve the subgrid space equation analytically. This allows to devise expressions for the ,stabilization parameter' ,, in the context of VMS (two-scale) method. The proposed method is equivalent to the traditional Green's method used in the literature to solve residual-free bubbles, although it offers another point of view, as the strong form of the subgrid scale equation is solved explicitly. In addition, the authors apply the methodology to high-order elements, namely quadratic and cubic elements. The proposed model consists in assuming that the subgrid scale vanishes also on interior nodes of the element and applying the strategy used for linear element in the segment between these interior nodes. The proposed scheme is compared with existing ones through the solution of a one-dimensional numerical example for linear, quadratic and cubic elements. In addition, the mesh convergence is checked for high-order elements through the solution of an exact solution in two dimensions. Copyright © 2008 John Wiley & Sons, Ltd. [source] A geometric-based algebraic multigrid method for higher-order finite element equations in two-dimensional linear elasticityNUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 7 2009Yingxiong Xiao Abstract In this paper, we will discuss the geometric-based algebraic multigrid (AMG) method for two-dimensional linear elasticity problems discretized using quadratic and cubic elements. First, a two-level method is proposed by analyzing the relationship between the linear finite element space and higher-order finite element space. And then a geometric-based AMG method is obtained with the existing solver used as a solver on the first coarse level. The resulting AMG method is applied to some typical elasticity problems including the plane strain problem with jumps in Young's modulus. The results of various numerical experiments show that the proposed AMG method is much more robust and efficient than a classical AMG solver that is applied directly to the high-order systems alone. Moreover, we present the corresponding theoretical analysis for the convergence of the proposed AMG algorithms. These theoretical results are also confirmed by some numerical tests. Copyright © 2008 John Wiley & Sons, Ltd. [source] | ||||||||||