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Finite element analysis. License. GNU Lesser General Public License 2.1 or later. Website. dealii .org. deal.II is a free, open-source library to solve partial differential equations using the finite element method. [1] [2] The current release is version 9.5, released in July 2023. [3]
Sheet metal forming, which is often referred to as stamping, is a process in which a piece of sheet metal, referred to as the blank, is formed by stretching between a punch and a die. The most painful and most frequent defects are wrinkles, thinning, springback and splits or cracks. Few methods are being used around the industry to cope with ...
GOMA is an open-source, parallel, and scalable multiphysics software package for modeling and simulation of real-life physical processes, with a basis in computational fluid dynamics for problems with evolving geometry. A generic finite element library written in C++ with interfaces for Python, Matlab and Scilab.
Mathematically, the vorticity of a three-dimensional flow is a pseudovector field, usually denoted by , defined as the curl of the velocity field describing the continuum motion. In Cartesian coordinates : In words, the vorticity tells how the velocity vector changes when one moves by an infinitesimal distance in a direction perpendicular to it.
Boussinesq approximation (buoyancy) In fluid dynamics, the Boussinesq approximation ( pronounced [businɛsk], named for Joseph Valentin Boussinesq) is used in the field of buoyancy -driven flow (also known as natural convection ). It ignores density differences except where they appear in terms multiplied by g, the acceleration due to gravity.
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Automatic differentiation. In mathematics and computer algebra, automatic differentiation ( auto-differentiation, autodiff, or AD ), also called algorithmic differentiation, computational differentiation, [1] [2] is a set of techniques to evaluate the partial derivative of a function specified by a computer program.
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Numerical simulation of the Fisher–KPP equation. In colors: the solution u(t,x); in dots : slope corresponding to the theoretical velocity of the traveling wave.. In mathematics, KPP–Fisher equation (named after Andrey Kolmogorov, Ivan Petrovsky, Nikolai Piskunov and Ronald Fisher) also known as the KPP equation, Fisher equation or Fisher–KPP equation is the partial differential equation:
Laplace–Beltrami operator. In differential geometry, the Laplace–Beltrami operator is a generalization of the Laplace operator to functions defined on submanifolds in Euclidean space and, even more generally, on Riemannian and pseudo-Riemannian manifolds. It is named after Pierre-Simon Laplace and Eugenio Beltrami .