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Schematic of D2Q9 lattice vectors for 2D Lattice Boltzmann. Unlike CFD methods that solve the conservation equations of macroscopic properties (i.e., mass, momentum, and energy) numerically, LBM models the fluid consisting of fictive particles, and such particles perform consecutive propagation and collision processes over a discrete lattice.
PISO algorithm (Pressure-Implicit with Splitting of Operators) was proposed by Issa in 1986 without iterations and with large time steps and a lesser computing effort.It is an extension of the SIMPLE algorithm used in computational fluid dynamics to solve the Navier-Stokes equations.
Ansys, Inc. is an American multinational company with its headquarters based in Canonsburg, Pennsylvania. It develops and markets CAE / multiphysics engineering simulation software for product design, testing and operation and offers its products and services to customers worldwide.
The first idea behind the Proper Orthogonal Decomposition (POD), as it was originally formulated in the domain of fluid dynamics to analyze turbulences, is to decompose a random vector field u(x, t) into a set of deterministic spatial functions Φ k (x) modulated by random time coefficients a k (t) so that:
Unlike earlier turbulence models, k-ε model focuses on the mechanisms that affect the turbulent kinetic energy. The mixing length model lacks this kind of generality. [2] The underlying assumption of this model is that the turbulent viscosity is isotropic, in other words, the ratio between Reynolds stress and mean rate of deformations is the same in all directions.
Video of spiral being propagated by level sets (curvature flow) in 2D.Left image shows zero-level solution. Right image shows the level-set scalar field. The Level-set method (LSM) is a conceptual framework for using level sets as a tool for numerical analysis of surfaces and shapes.
The Functional Mock-up Interface (or FMI) defines a standardized interface to be used in computer simulations to develop complex cyber-physical systems.. The vision of FMI is to support this approach: if the real product is to be assembled from a wide range of parts interacting in complex ways, each controlled by a complex set of physical laws, then it should be possible to create a virtual ...
A comparison of the convergence of gradient descent with optimal step size (in green) and conjugate vector (in red) for minimizing a quadratic function associated with a given linear system. Conjugate gradient, assuming exact arithmetic, converges in at most n steps, where n is the size of the matrix of the system (here n = 2).