Numerical methods for partial differential equations is the branch of numerical analysis that studies the numerical solution of partial differential equations (PDEs).
COMSOL Multiphysics is a finite element analyzer, solver, and simulation software package for various physics and engineering applications, especially coupled phenomena and multiphysics. The software facilitates conventional physics-based user interfaces and coupled systems of partial differential equations (PDEs). COMSOL Multiphysics provides an IDE and unified workflow for electrical, mechanical, fluid, acoustics, and chemical applications.
Mesh generation is the practice of creating a mesh, a subdivision of a continuous geometric space into discrete geometric and topological cells. Often these cells form a simplicial complex. Usually the cells partition the geometric input domain. Mesh cells are used as discrete local approximations of the larger domain. Meshes are created by computer algorithms, often with human guidance through a GUI, depending on the complexity of the domain and the type of mesh desired. A typical goal is to create a mesh that accurately captures the input domain geometry, with high-quality (well-shaped) cells, and without so many cells as to make subsequent calculations intractable. The mesh should also be fine in areas that are important for the subsequent calculations.
Fluid–structure interaction (FSI) is the interaction of some movable or deformable structure with an internal or surrounding fluid flow. Fluid–structure interactions can be stable or oscillatory. In oscillatory interactions, the strain induced in the solid structure causes it to move such that the source of strain is reduced, and the structure returns to its former state only for the process to repeat.
A CFD-DEM model is suitable for the modeling or simulation of fluid-solids or fluid-particles systems. In a typical CFD-DEM model, the phase motion of discrete solids or particles is obtained by the Discrete Element Method (DEM) which applies Newton's laws of motion to every particle and the flow of continuum fluid is described by the local averaged Navier–Stokes equations that can be solved by the traditional Computational Fluid Dynamics (CFD). The model is first proposed by Tsuji et al. The interactions between the fluid phase and solids phase is better modeled according to Newton's third law.
The FEniCS Project is a collection of free and open-source software components with the common goal to enable automated solution of differential equations. The components provide scientific computing tools for working with computational meshes, finite-element variational formulations of ordinary and partial differential equations, and numerical linear algebra.
The finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical problem areas of interest include the traditional fields of structural analysis, heat transfer, fluid flow, mass transport, and electromagnetic potential. Computers are usually used to perform the calculations required. With high-speed supercomputers, better solutions can be achieved, and are often required to solve the largest and most complex problems.
code_saturne is a general-purpose computational fluid dynamics free computer software package. Developed since 1997 at Électricité de France R&D, code_saturne is distributed under the GNU GPL licence. It is based on a co-located finite-volume approach that accepts meshes with any type of cell and any type of grid structure.
Image-based meshing is the automated process of creating computer models for computational fluid dynamics (CFD) and finite element analysis (FEA) from 3D image data. Although a wide range of mesh generation techniques are currently available, these were usually developed to generate models from computer-aided design (CAD), and therefore have difficulties meshing from 3D imaging data.
Synopsys Simpleware ScanIP is a 3D image processing and model generation software program developed by Synopsys Inc. to visualise, analyse, quantify, segment and export 3D image data from magnetic resonance imaging (MRI), computed tomography (CT), microtomography and other modalities for computer-aided design (CAD), finite element analysis (FEA), computational fluid dynamics (CFD), and 3D printing. The software is used in the life sciences, materials science, nondestructive testing, reverse engineering and petrophysics.
Gmsh is a finite-element mesh generator developed by Christophe Geuzaine and Jean-François Remacle. Released under the GNU General Public License, Gmsh is free software.
KIVA is a family of Fortran-based computational fluid dynamics software developed by Los Alamos National Laboratory (LANL). The software predicts complex fuel and air flows as well as ignition, combustion, and pollutant-formation processes in engines. The KIVA models have been used to understand combustion chemistry processes, such as auto-ignition of fuels, and to optimize diesel engines for high efficiency and low emissions. General Motors has used KIVA in the development of direct-injection, stratified charge gasoline engines as well as the fast burn, homogeneous-charge gasoline engine. Cummins reduced development time and cost by 10%–15% using KIVA to develop its high-efficiency 2007 ISB 6.7-L diesel engine that was able to meet 2010 emission standards in 2007. At the same time, the company realized a more robust design and improved fuel economy while meeting all environmental and customer constraints.
Gerris is computer software in the field of computational fluid dynamics (CFD). Gerris was released as free and open-source software, subject to the requirements of the GNU General Public License (GPL), version 2 or any later.
SU2 is a suite of open-source software tools written in C++ for the numerical solution of partial differential equations (PDE) and performing PDE-constrained optimization. The primary applications are computational fluid dynamics and aerodynamic shape optimization, but has been extended to treat more general equations such as electrodynamics and chemically reacting flows. SU2 supports continuous and discrete adjoint for calculating the sensitivities/gradients of a scalar field.
MOOSE is an object-oriented C++ finite element framework for the development of tightly coupled multiphysics solvers from Idaho National Laboratory. MOOSE makes use of the PETSc non-linear solver package and libmesh to provide the finite element discretization.
Nektar++ is a spectral/hp element framework designed to support the construction of efficient high-performance scalable solvers for a wide range of partial differential equations (PDE). The code is released as open-source under the MIT license. Although primarily driven by application-based research, it has been designed as a platform to support the development of novel numerical techniques in the area of high-order finite element methods.
CONSELF is a computer-aided engineering (CAE) platform used by engineers for design purposes. The platform, which highly relies on cloud computing, is developed by CONSELF SRL since its first release in October 2015. In March 2016 a new release of the platform defined guided workflows for the users with focus on turbomachinery, fire scenarios and flows with dispersed solid particles. Through the platform it is possible to run both Computational Fluid Dynamics and Finite Element Analysis. Among the solvers and libraries used by CONSELF platform, a number of open-source technologies are included, such as:
