Theory NOGRID Simulation Solver Technology

The fundamental basis of almost all CFD problems are the Navier–Stokes equations, which are a statement of the balance of momentum, but sometimes the equations for conservation of mass and the balance of energy are added.

In order to solve the Navier–Stokes equations the fluid domain must be discretized, which means the volume occupied by the fluid is divided into discrete cells (the mesh). The Finite Volume Method (FVM) is a common approach used in CFD codes, as it has an advantage in memory usage and solution speed, especially for large problems, high Reynolds number turbulent flows and source term dominated flows (like combustion). The Finite Element Method (FEM) is used in structural analysis of solids, but is also applicable to fluids. The Finite Difference Method (FDM) has historical importance and is easy to implement. It is currently only used in few specialized codes, which handle complex geometry with high accuracy and efficiency.

Figure 1: Navier-Stokes Equations

MESHLESS MODELING AND SIMULATION

Numerical fluid mechanics (Computational Fluid Dynamics, CFD) is a well known and established method within fluid mechanics and is used to solve fluid mechanical problems approximately with numerical methods. The model equations are the Navier-Stokes equations, which are nonlinear partial differential equations of second order, that prescribe a fluid completely.
An important step in handling partial differential equations is to use discrete algebraic replacements for the continuous differential equations. Several methods are currently in use, such as the finite volume (FV), finite element (FE), and finite difference (FD) method. We use a general finite difference (gFD) method to discretize the Navier-Stokes equation. General means that we operate on an unstructured points basis, whereas the classical FD-method operates on structured points only.

method01

Figure 2: Point cloud versus finite element mesh

Our meshless CFD software NOGRID points, as well as NOGRID pointsBlow, is based on the Finite Pointset Method, a method, which generates a local defined, non-stationary point cloud distribution for discretization of the Navier-Stokes equations. The method itself is based on the general finite difference method and the key features are:

Instead of a mesh NOGRID points discretizes the continuum domain by a point cloud
The point density is prescribed by a smoothing length defined locally and can vary from one time step to another
NOGRID points does not use a rigid neighborhood list for a certain point (=node) as it is required in a mesh based method. All neighbors are allowed to move and the neighborhood list is recomputed at each time step

Thus, the simple idea of the NOGRID method is to use a dynamical discretization method.

The point cloud is generated automatically by the software depending on user's settings. That's why there is no need to generate a mesh as required in classical CFD methods. NOGRID finite points are automatically filled, moved, refilled and cleaned depending on user specifications. The point cloud can be defined variously, e.g. constant in the whole flow domain, changing with time or increasing/decreasing locally depending on the flow/geometry situation.

Why choose Nogrid?

NOGRID provides professional CFD software for the simulation of fluid flow, heat and mass transfer, and chemical reactions. Its efficient modelling workflow helps engineers analyse flow behaviour, evaluate designs and make informed decisions without creating a conventional volume mesh.

Faster model preparation

With NOGRID, only the geometry boundary needs to be meshed. The finite points inside the fluid domain are generated automatically according to user-defined settings, both at the start of the simulation and during the calculation.

This approach reduces preprocessing effort and makes it easier to prepare complex geometries and cavities for simulation.

Efficient CFD workflow

The modelling process follows four straightforward steps:

Build the geometry. Mesh the boundary. Define the simulation. Start the calculation.

NOGRID is designed to provide short computation times, including for applications involving complex cavities. Engineers can use the resulting data to examine flow distribution and other relevant flow characteristics.

Better insight into fluid-flow processes

CFD solves the fundamental equations governing fluid flow. NOGRID software enables engineers to predict and analyse the behaviour of fluids and related physical processes before or alongside physical testing.

The simulation results can support:

evaluation and comparison of design alternatives
optimisation of construction and operating parameters
improved planning reliability
reduction of development time and testing effort
faster progression from design to market or operation

Steps from geometry generation to simulation results

TRAINING

Our two-day training courses teach participants how to set up, run and evaluate simulations efficiently with NOGRID CFD software. The courses include practical guidance for handling different types of simulation cases.

For more details please refer to Training Courses →

Technical Support

Professional support is available from the beginning of your work with NOGRID. Our technical team assists users by telephone and email with software operation, case setup and simulation-related questions.

For more details please refer to Software Support →

Simulation Service

When internal time, expertise or resources are limited, NOGRID can support your project with individual numerical simulation services. Our engineers develop and evaluate CFD models based on the specific requirements of your application.