 # Modeling & Numerical Simulation Modeling and Numerical Simulation is a powerful tool that allows engineers to better understand product performance, achieve optimized designs faster, and release products to market earlier. Modeling and Simulation also allows an understanding of failure, which is paramount to managing risks such as: safety, warranty issues, and future research and development efforts.

WESTEST contracts PAMI skilled engineers and experts to perform modeling and numerical simulation. These experts, including Dr. Hubert Landry, have vast modeling and simulation experience and expertise in a multitude of industries.

SolidWorks3D is used for most modelling and simulation projects, which is CAD software. SOLIDWORKS allows us to build 3D models of mechanical parts and create fabrication drawings. Beginning the process with CAD models can be helpful for simulations with other software tools.

## Finite Element Method (FEM)

The Finite Element Method (also known as Finite Element Analysis or FEA) is the application of the numerical solving of the discretized physical and mathematical model. It is employed for solid mechanics and structural problems. The key is to break down the real system (complex) into multiple smaller bodies or units (finite elements; elements that are finite in size in contrast to the continuum of the real system). The finite elements are interconnected at points called nodes. The nodes are the discrete points on the physical part where the analysis predicts the response of the part due to applied loading. All the elements form the finite element mesh and contain the material and structural properties of the model, defining how it will react to certain conditions.

FEM Specialized Software: Autodesk Simulation Mechanical

## Computational Fluid Dynamics (CFD)

Fluid flows are governed by partial differential equations (PDEs) that represent conservation laws for the mass, momentum and energy (the mathematical model). The CFD method consists of replacing the system of PDEs by a set of algebraic equations which can be solved numerically by a computer. The same process of approximating the governing equations by simple functions, followed by the division of the domain in smaller units (discretization) and then the equations are solved numerically using initial and boundary conditions. The physical phenomena involved in fluid flow are complex and nonlinear so an iterative solution approach is required.

CFD Specialized Software:  STAR-CCM+

## Discrete Element Method (DEM)

For granular and discontinuous materials, the best approach is to use the discrete element method (DEM), a numerical method for computing the motion of large numbers of particles. DEM considers a system as a collection of discrete entities providing knowledge of the particle behaviour at the micro scale, enabling a better prediction and understanding of the macro scale (the bulk system). DEM calculates the sum of the forces acting on the particles and integrates Newton’s equation of motion to obtain velocity and position at the next time step. In doing so, the DEM describes the path of every particle in the assembly as time proceeds. The DEM is all about contacts and collisions (particles with particles as well as particles with the physical domain); the time-stepping algorithm used to generate the solution is very computationally demanding.

DEM Specialized Software: EDEM

## Rigid Body Dynamics (RBD)

Rigid body dynamics simulations are concerned with the movement of systems of interconnected bodies under the action of external forces. Because the bodies are considered rigid, they do not deform during the simulation which simplifies the simulation. Collisions are however important as they can impact how the system behaves. The simulation requires solving the equations of motion that are formulated from information on each rigid body (mass, center of mass, inertia tensor) and interaction conditions between bodies (forces, constraints). The same multibody dynamics (MBD) is often seen, and it generally implies going beyond the motion and interactions of rigid bodies to include actuation and control. The loads generated by an MBD analysis can be used in an FEA.

## Multiphysics Systems

In industry, a large proportion of systems involved more than one physical phenomenon. A relatively recent trend in the world of numerical simulations is the coupling of two (and sometimes multiple) methods. The simple form of a multiphysics analysis is done by doing sequential simulations when the output of one analysis informs the following analysis in the form of initial or boundary conditions. More often than not, the physical phenomena are strongly coupled requiring concurrent simulations that exchange data on the go. The system of interest may involve the movement of particles in air as in pneumatic conveying in which case, a coupled DEM-CFD approach may be appropriate. The field of fluid-structure interactions (FSI) has also emerged, where the interest is in the loading and deformation of structures as influenced by fluid flows. In turn, the flow fields may change as a result of the displacement or deformation of the structure.  Heat generation and cooling applications are also examples of multiphysics problems.

----

FREE DOWNLOAD: Modeling and Numerical Simulation Software White Paper, by Dr. Hubert Landry

----