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Numerical Methods for Convection Heat Transfer
Published in Yogesh Jaluria, Kenneth E. Torrance, Computational Heat Transfer, 2017
Yogesh Jaluria, Kenneth E. Torrance
Because of the less sparse form of FEM matrices, due to the use of irregular grids and higher order polynomial interpolations, recent efforts have focused on improving the computational ef ciency of FEM simulation by using approaches used earlier in other methods. One of these methods is the projection method where velocity is uncoupled from pressure so that a sequential solution of velocity, followed by that for pressure, is used, rather than simultaneously solving the coupled set. Other sequential solution strategies have been developed. For transient problems, the viscous terms may be treated implicitly and the convection terms explicitly to obtain smaller symmetric linear systems which can be solved ef ciently. Similarly, many other advancements and extensions have been obtained in recent years to improve the ef ciency and reduce the storage requirements of FEM analysis of complicated problems. These advances make it easy to develop general purpose computer codes based on nite element methods and thus effectively use the versatility and exibility of these methods for simulating thermal systems and processes.
Discrete Methods for Elliptic Problems
Published in Victor S. Ryaben’kii, Semyon V. Tsynkov, A Theoretical Introduction to Numerical Analysis, 2006
Victor S. Ryaben’kii, Semyon V. Tsynkov
The foregoing analysis does not imply, of course, that if one variational formulation does not work for a given problem, then others will not work either. The example of the Helmholtz equation does indicate, however, that it may be worth developing a more general method that would apply to problems for which no variational formulation (like the one from Section 12.2.1) is known. A method of this type was proposed by Galerkin in 1916. It is often referred to as the projection method.
Placement of ultra-high performance concrete for inclined-surface pavement
Published in Road Materials and Pavement Design, 2021
Tae Yong Shin, Jae Hong Kim, Kyung-Taek Koh, Gum-Sung Ryu, Kejin Wang
The governing equation of the CFD simulation is given by the incompressible steady-state momentum equation, where V is an arbitrary control volume with its bounding surface area S, n is the outward normal vector to S. External force is described by the hydrostatic pressure p, the viscous shear stress τ, and the body force f. The fluid to be simulated is characterised by its density and its velocity field ρ and v, respectively. To solve a time-dependent incompressible flow problem, the projection method has been widely used in engineering applications. The basic concept for projection method is the legitimate segregation of pressure and velocity fields for efficient solution of the incompressible Navier-Stokes equation. In this study, a second-order projection method supported by ABAQUS/CFD was adopt with no turbulence. Considering the momentum increment and the velocity of the moving mesh, if any, allows us to analyze the transient response of the model.