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hexameshing of 2D elbow pipe

hexameshing of 2D elbow pipe

This tutorial demonstrates how to do the following:• Block the geometry.• Associate entities to the geometry.• Move vertices onto the geometry.• Apply mesh parameters.• Generate the initial mesh.• Refine the mesh. Blocking Strategy The blocking strategy for the 2D pipe geometry involves creating a T-shaped blocking and fitting it to the geometry. The 2D pipe …

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CFD 18 : Numerical Discretizations Techniques: Finite Element,Finite Difference , Spatial

CFD 18 : Numerical Discretizations Techniques: Finite Element,Finite Difference , Spatial

Discretization can be understood as replacement of an exact solution of a PDE or a system of PDEs in a continuum domain by an approximate numerical solution in a discrete domain. Instead of continuous distributions of solution variables we find a finite set of numerical values that represent an approximation of the solution.

CFD 17 : Elliptical Equations

CFD 17 : Elliptical Equations

The elliptic equations do not have real characteristics at all. Effect of any perturbation is felt immediately and to full degree in the entire domain of solution. There are no limited domains of influence or dependence

Physically, the elliptic systems describe equilibrium distributions of properties in spatial domains with boundary conditions

The elliptic PDE problems are always of equilibrium type. The solution has to be found at once in the entire domain space.

CFD 16 : Parabolic Equations

CFD 16 : Parabolic Equations

The parabolic equations of second order have only one family of real characteristics as case of b^2-4AC = 0 . For example, for the one-dimensional heat equation, the slope is

CFD 15: Hyperbolic Equations

CFD 15: Hyperbolic Equations

There are two families of characteristics: left-running x + at = const and right-running x − at = const.

It can be shown that the general solution of equation can be represented as

CFD 14 : Mathematical Classification of PDE of Second Order

CFD 14 : Mathematical Classification of PDE of Second Order

The quasilinear PDE can be classified into three types according to the existence and form of their characteristics, the special lines in the solution domain. . One aspect is, however, very important for us: The information in the solutions tends to propagate along the characteristics if they exist. This has deep implications not only for the mathematical properties of the solution but also for the choice of numerical methods. To put it simply, different numerical methods must be used for equations of different types.

CFD 13 : Formulation of PDEs

CFD 13 : Formulation of PDEs

In this case, we disregard temperature variations across the rod and assume that the temperature T is a function of the coordinate x and time t . The solution domain consists of the space interval [0, x] and the time interval, which can be finite [t(0), t(end)] or extended to infinity [t(0),∞). Different kinds of boundary conditions are possible. The situation when the ends of the rod are kept at constant temperature corresponds to the Dirichlet boundary conditions

CFD 12 : Equilibrium and Marching Problems

CFD 12 : Equilibrium and Marching Problems

In principle, all fluid flow and heat transfer processes evolve with time. From the practical viewpoint, it is, however, desirable to classify them into two groups: equilibrium (time-independent) and transient (time-evolving)

CFD 11 : dirichlet & Neumann boundary Conditions

CFD 11 : dirichlet & Neumann boundary Conditions

The main entity of the PDE analysis is not a separate equation but a complete PDE problem consisting of an equation, domain of solution, boundary and initial conditions. The problem has to be solved in a spatial domain and, in the case of time-dependency, in a time interval between t(0) and t(end) . tend can be a finite number or infinity. Similarly, the domain may have a finite size or extend to infinity in one or several directions. In numerical simulations, the infinite limits of the spatial or time domain are replaced by sufficiently large finite numbers.Boundary conditions have to be imposed at the boundaries of the spatial domain Ω,

CFD 10 : Partial Differential Equations (PDEs)

CFD 10 : Partial Differential Equations (PDEs)

From the mathematical viewpoint, the equations of fluid flows and heat transfer are partial differential equations (PDE).

Certain properties of the equations have profound effect on the behavior of solutions and, significantly for us, on the choice
of numerical method.

CFD 9 : Boundary Conditions – Wall and Inlet/exit

CFD 9 : Boundary Conditions – Wall and Inlet/exit

In principle, one can say that all parts of the universe are connected to each other by fluxes of heat and mass and, thus, must be included into a good CFD solution. Since such an enterprise is hardly feasible, we have to compromise and formulate CFD problems for finite domains limited by boundaries. Such boundaries …

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CFD 8 : Conservation of Energy

CFD 8 : Conservation of Energy

The energy conservation principle can be formulated for a fluid element in the manner similar to the mass and momentum conservation as