A discrete element method (DEM), also called a distinct element method, is any of a family of numerical methods for computing the motion and effect of a large number of small particles. Though DEM is very closely related to molecular dynamics, the method is generally distinguished by its inclusion of rotational degrees-of-freedom as well as stateful contact and often complicated geometries. With advances in computing power and numerical algorithms for nearest neighbor sorting, it has become possible to numerically simulate millions of particles on a single processor. Today DEM is becoming widely accepted as an effective method of addressing engineering problems in granular and discontinuous materials, especially in granular flows, powder mechanics, and rock mechanics. DEM has been extended into the Extended Discrete Element Method taking heat transfer, chemical reaction and coupling to CFD and FEM into account.
Computational fluid dynamics (CFD) is a branch of fluid mechanics that uses numerical analysis and data structures to analyze and solve problems that involve fluid flows. Computers are used to perform the calculations required to simulate the free-stream flow of the fluid, and the interaction of the fluid with surfaces defined by boundary conditions. With high-speed supercomputers, better solutions can be achieved, and are often required to solve the largest and most complex problems. Ongoing research yields software that improves the accuracy and speed of complex simulation scenarios such as transonic or turbulent flows. Initial validation of such software is typically performed using experimental apparatus such as wind tunnels. In addition, previously performed analytical or empirical analysis of a particular problem can be used for comparison. A final validation is often performed using full-scale testing, such as flight tests.
Numerical methods for partial differential equations is the branch of numerical analysis that studies the numerical solution of partial differential equations (PDEs).
The boundary element method (BEM) is a numerical computational method of solving linear partial differential equations which have been formulated as integral equations, including fluid mechanics, acoustics, electromagnetics, fracture mechanics, and contact mechanics.
Computational electromagnetics (CEM), computational electrodynamics or electromagnetic modeling is the process of modeling the interaction of electromagnetic fields with physical objects and the environment using computers.
Multiscale modeling or multiscale mathematics is the field of solving problems that have important features at multiple scales of time and/or space. Important problems include multiscale modeling of fluids, solids, polymers, proteins, nucleic acids as well as various physical and chemical phenomena.
Computational mechanics is the discipline concerned with the use of computational methods to study phenomena governed by the principles of mechanics. Before the emergence of computational science as a "third way" besides theoretical and experimental sciences, computational mechanics was widely considered to be a sub-discipline of applied mechanics. It is now considered to be a sub-discipline within computational science.
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.
In the field of numerical analysis, meshfree methods are those that do not require connection between nodes of the simulation domain, i.e. a mesh, but are rather based on interaction of each node with all its neighbors. As a consequence, original extensive properties such as mass or kinetic energy are no longer assigned to mesh elements but rather to the single nodes. Meshfree methods enable the simulation of some otherwise difficult types of problems, at the cost of extra computing time and programming effort. The absence of a mesh allows Lagrangian simulations, in which the nodes can move according to the velocity field.
This is an alphabetical list of articles pertaining specifically to Engineering Science and Mechanics (ESM). For a broad overview of engineering, please see Engineering. For biographies please see List of engineers and Mechanicians.
Computational Engineering is an emerging discipline that deals with the development and application of computational models for engineering, known as Computational Engineering Models or CEM. Computational engineering uses computers to solve engineering design problems important to a variety of industries. At this time, various different approaches are summarized under the term Computational Engineering, including using computational geometry and virtual design for engineering tasks, often coupled with a simulation-driven approach In Computational Engineering, algorithms solve mathematical and logical models that describe engineering challenges, sometimes coupled with some aspect of AI, specifically Reinforcement Learning.
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 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.
ADINA is a commercial engineering simulation software program that is developed and distributed worldwide by ADINA R & D, Inc. The company was founded in 1986 by Dr. Klaus-Jürgen Bathe, and is headquartered in Watertown, Massachusetts, United States. On April 7, 2022, Bentley Systems acquired ADINA R&D, Inc.
The extended discrete element method (XDEM) is a numerical technique that extends the dynamics of granular material or particles as described through the classical discrete element method (DEM) by additional properties such as the thermodynamic state, stress/strain or electro-magnetic field for each particle. Contrary to a continuum mechanics concept, the XDEM aims at resolving the particulate phase with its various processes attached to the particles. While the discrete element method predicts position and orientation in space and time for each particle, the extended discrete element method additionally estimates properties such as internal temperature and/or species distribution or mechanical impact with structures.
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.
FEATool Multiphysics is a physics, finite element analysis (FEA), and partial differential equation (PDE) simulation toolbox. FEATool Multiphysics features the ability to model fully coupled heat transfer, fluid dynamics, chemical engineering, structural mechanics, fluid-structure interaction (FSI), electromagnetics, as well as user-defined and custom PDE problems in 1D, 2D (axisymmetry), or 3D, all within a graphical user interface (GUI) or optionally as script files. FEATool has been employed and used in academic research, teaching, and industrial engineering simulation contexts.
In geology, numerical modeling is a widely applied technique to tackle complex geological problems by computational simulation of geological scenarios.
