UNIT-V

FIELD PROBLEM AND METHODS OF SOLUTIONS

Modes of Heat Transfer Heat, by definition, is the energy in transit due to temperature difference. Whenever

exists a temperature difference in a medium or between media, heat flow must. Different types of heat transfer processes are called modes. When a Temperature gradient exists in a stationary medium, which may be a solid or a fluid, heat flows under the law of conduction heat transfer. On the other hand if the temperature gradient exists between a surface and a moving fluid we use the term Convection. The third mode of heat transfer is termed Radiation and it needs no medium to transfer through since it is driven by electromagnetic waves emitted from all surfaces of finite temperature, so there is a net heat transfer by radiation between two surfaces at different temperatures

FREE/OPEN SOURCE FEA SOFTWARES:

Name Description License Operating System

Agros2DMultiplatform open source application for the solution of physical problems based on the Hermes library

GNU GPL Linux, Windows

CalculiX

It is an Open Source FEA project. The solver uses a partially compatible ABAQUS file format. The pre/post-processor generates input data for many FEA and CFD applications

GNU GPL Linux, Windows

Code Aster

is an Open Source software package for Civil and Structural Engineering finite element analysis and numeric simulation in structural mechanics which is written in Python and Fortran

GNU GPL Linux, FreeBSD

Conceptsis an Open Source software package C/C++ hp-FEM/DGFEM/BEM library for elliptic equations

GNU GPL Mac OS X, Windows

deal.IIComprehensive set of tools for finite element codes, scaling from laptops to clusters with 10,000+ cores. Written in C++.

QPL up to release 7.2, LGPL after that

Linux, Unix, Mac OS X, Windows

DUNE Distributed and Unified Numerics Environment, written in C++

GPL Version 2 with Run-Time Exception

Linux, Unix, Mac OS X

Elmer Open source multiphysical simulation software developed by Finnish Ministry of Education's CSC, written primarily in

GPL Linux, Mac OS X, Windows

Name Description License Operating System

Fortran (written in Fortran90, C and C++)

FEATFLOWSubroutine system for the numerical solution of the incompressible Navier-Stokes equations in two and three space dimensions

Non Commercial Fortran

FEATool Easy to Use Matlab and Octave Multiphysics FEM Solver and GUI Toolbox

Non Commercial

Linux, Unix, Mac OS X, Windows

FEBio Finite Elements for Biomechanics Custom Linux, Mac OS X, Windows

FEniCS Project

Software package developed by American and European researchers with the goal to enable automated solution of differential equations

LGPL (Core) & GPL/LGPL (Non-Core)[1]

Linux, Unix, Mac OS X, Windows

FreeFem++

Software written in C++ for rapid testing and finite element simulations. The problem is defined in terms of its variational formulation

GPLLinux, Mac OS X, Windows, Solaris

GetFEM++

A generic finite element library written in C++ with interfaces for Python, Matlab and Scilab. It focuses on modeling of contact mechanics and discontinuities (e.g. cracks).

LGPL Unix, Mac OS X, Windows

Hermes ProjectModular C/C++ library for rapid development of space- and space-time adaptive hp-FEM solvers

LGPLLinux, Unix, Mac OS X, Windows

jFEM2D/3D open source C++ FEM codes developed for nanophotonics by Jeffrey M. McMahon [2][3]

GNU GPL

Linux, Unix, Mac OS X, (Windows, but unsupported)

MoFEM JosePHMoFEM (JosePH) is a finite element analysis code tailored for the solution of multi-physics problems

LGPL Unix, Linux, Mac OS X

MOOSE

Multiphysics Object Oriented Simulation Environment - an object oriented C++ finite element framework for rapid development of tightly coupled multiphysics solvers

LGPL Unix, Linux, Mac OS X

OOFEM Object Oriented Finite EleMent solver, written in C++ GPL Version 2 Unix, Windows

OpenFOAM (Field Operation And Manipulation)

Originally for CFD only, but now includes finite element analysis through tetrahedral decomposition of arbitrary grids

GPL Unix, Linux

OpenSees is an Open System for Earthquake Engineering Simulation

Non Commercial

Unix, Linux, Windows

Name Description License Operating System

SfePy

SfePy is a software for solving systems of coupled partial differential equations (PDEs) by the finite element method in 2D and 3D. It can be viewed both as black-box PDE solver, and as a Python package which can be used for building custom applications. The time demanding parts implemented in C/Cython.[4]

BSD Unix, Linux, Windows

SU2 code

Primary applications are computational fluid dynamics and aerodynamic shape optimization,[5] but has been extended to treat more general equations such as electrodynamics and chemically reacting flows.

GNU Lesser General Public License, version 2.1

Unix, Linux, OS X, Windows

Z88/Z88Aurora

Freeware finite element package; The present version Z88Aurora V3 offers, in addition to static strength analysis modules such as non-linear strength calculations (large displacements), simulations with non-linear materials, natural frequency and static thermal analysis.

CustomLinux, Windows, Mac OS X

SOURCE OF ERROR

Four primary sources of error are: (I)ROUNDOFF ERROR(II)TRUNCATION ERROR,(III)TERMINATION OF ITERATIONS IV)STATISTICAL ERROR

We will estimate the sizes of these errors, either a priori from what we know in advance about the solution, or a posteriori from the computed (approximate) solutions themselves. Software development requires distinguishing these errors from those caused by outright bugs. In fact, the bug may not be that a formula is wrong in a mathematical sense, but that an approximation is not accurate enough. The floating point computer arithmetic and the IEEE floating point standard. The others are treated later. Scientific computing is shaped by the fact that nothing is exact. A mathematical formula that would give the exact answer with exact inputs might not be robust enough to give an approximate answer with (inevitably) approximate inputs. Individual errors that were small at the source might combine and grow in the steps of a long computation. Such a method is unstable. A problem is ill conditioned if any computational method for it is unstable. Stability theory, which is modeling and analysis of error growth, is an important part of scientific computing.