Research and Development at NOGRID

In engineering, fluid-structure coupling or fluid-structure interaction (FSI) refers to the consideration of the mutual influence of structure and flow. The mutual influence of structure and flow is an interesting phenomenon that often occurs in nature and technology. It occurs on deformable and/or movable structures around or through the fluid flows. The structure deforms under the forces imposed by the flow. In the case of highly deformable structures, the flow is very often disturbed by the structure and thus influenced. In this case, there is a real, two-sided fluid-structure coupling.

NOGRID points, based on FPM (Finite Pointset Method), is a meshless CFD software package for simulation tasks in the wide area of flow and continuum mechanical problems. The software is a gridfree or meshfree method which, in contrast to classical numerical methods, such as Finite Elements or Finite Volumes, does not require a grid or mesh. The software can excellently be applied in the case of all problems, where grid-based methods reach their limits due to the necessary remeshing.

Our research group works on solutions for processes where the dynamic interaction between fluid flow and solid deformation is important and where deformable structures need special treatments in terms of physical properties and dimensions. Biology provides numerous examples of FSI where the structure is flexible and deformable and often very thin compared to the dimensions of the flow area.

The field of rheology covers the behavior of perfectly viscous liquid (Newtonian fluid) materials and perfect elastic solid (Hookean solid) material, as depicted in Figure 2. Generally, fluids are categorized as Newtonian or non-Newtonian. In classical fluid dynamics the fluid is in general Newtonian, the deviatoric stress tensor being directly proportional to the strain rate tensor; the constant of proportionality may depend on temperature or solute concentration, but not on strain rate. Examples of Newtonian fluids are water, glycerol, alcohol, thin motor oil, and air. However, many everyday fluids are non-Newtonian, being shear-thinning, shear-thickening or viscoelastic. Examples are ketchup, starch, egg white, custard, cake batter, shampoo, paint, blood, suspension or granular media. So, what is the constitutive relation between stress and strain rate that should replace the Newtonian relation, and what are the consequences for the flow patterns and the forces exerted on solid boundaries?
Understanding the macro-scopic properties of the fluid from a mechanistic description of its microstructure is a problem of fundamental importance and great difficulty. Continuum modelling of granular media is particularly difficult when the grains are irregular, and the gap between experimental data and theoretical or computational prediction remains wide. Very often the mathematical formulation is known but the macroscopic physical processes are complex and often not well understood. Furthermore the model equations that have been proposed are difficult to solve and CFD standard methods generally do not work for this class of problems.

The production and processing steps leading to a finished product employing advanced materials are most often carried out via deformation and flow in the liquid state. Although largely empirical procedures have historically been used in the design of new processes, future economic competition, as well as requirements for improved product quality, reproducibility and precision, all demand the development of a deductive basis for process design and control.
For example, the inability to predict the behavior of polymer liquids in an extrusion molding process precludes prediction of the final shape of the solidified product --- thus the design of each mold must be done by a trial and error.
Qualitative phenomena observed in non-Newtonian flow experiments are often dramatically different from expectations based on similar observations for small-molecule liquids. Development of new experimental techniques are needed to provide much more comprehensive characterization of the rheological behavior of complex fluids, and for characterizing the microstructural state of a non-Newtonian liquid undergoing a flow, since this determines the properties of any product which results from the flow process.

The behavior of a liquid on small scales can differ significantly from its behavior on large scales. So, in Microfluidics, typically below sub-millimeter, surface and interface effects dominate the dynamics and induce, for example, Marangoni currents or interface instabilities. The viscous forces are significantly larger in relation to the inertial forces. This is expressed by the Reynolds number, which is usually less than 1. The flow is thus laminar and in some cases the inertial forces can be completely neglected. Then there is a so-called Stokes flow or creeping flow. The corresponding equations are then mostly linear and easier to solve than the complete Navier-Stokes equations. The simulation of stirring and mixing processes in microfluidics is a very interesting field of research, since the mixing success can only be controlled via expansion and folding processes in addition to diffusion. Furthermore, diffusion processes in microfluidic systems are slow and special attention must be paid to the transport of chemical substances in microfluidic systems. Microfluidic applications range from lab-on-a-chip technology to inkjet printing to coating flows and biomedical diagnostics.

Research at NOGRID covers the fundamental principles of low Reynolds number flows, including the governing equations. The special focus of our research is on the simulation of stirring and mixing processes in microfluidics.

Multi-phase flows are relevant to many industrial applications. One important issue associated with multi-phase flows is the broad range of length scales of the dynamically evolving material interface. For example, in the mixing process (see Figure 4), though the initial interface is well resolved at the early stage, small unresolved interface structures are produced continuously. With a given spatial-temporal resolution limit these resolved and unresolved interface scales usually coexist. Therefore, an efficient numerical modeling method is required to cope both resolved and unresolved interface scales.
Those flows involving two or more fluids that do not mix, or may mix a little, are called two-phase or multi-phase flows. Multiphase flows are inherently multiscale because the physic of the problem is not only driven by the mean flow, but also by the interface, which dimension can be smaller by orders of magnitude.

“Multi-scale” means flow tasks with several separated dominant scales or with a large range of continuous scales. This multi-scale issue is critical because the computational efficiency is usually determined by the ratios of resolved length or time scales. So, in recent years, there has been a tremendous growth of activity on multiscale modeling and computation. In particular, the multiscale hybrid numerical methods are those that combine multiple models defined at fundamentally different length and time scales within the same overall spatial and temporal domain. Processes that span wide-ranging time and space scales are encountered in science and engineering in a vast number of fundamental and applied contexts:

• coupled flow between air (low viscosity) and viscous liquids like glass, polymer, lava, etc.  (high viscosity), where the fluids acts on different time scales
• forming processes starting from 3D flow area ending in a 2D flow area or vice versa
• injection molding with 3D, 2D or 1D areas (computing entire domain in 3D would increase the computation time dramatically)
• modelling thin flexible membranes as flow boundary
• efficient mixing of particles or powders in the food and pharmaceutical industries
• dislocation creep and crack propagation in failing materials
• large-scale atmospheric circulation
• atmospheric chemistry including the transport and mixing of pollutants
• ocean or coastal flows

The challenge of understanding and predicting these multiscale processes, particularly those in the field of fluid dynamics, is one of the core motivation of the NOGRID research group. For that reason a framework of hybrid continuum multiscale methods will be developed to simulate such multi-scaled fluid flows.

In many applications of numerical simulation, for example fluid and structural mechanics, the structures and geometries are discretized by complex grids or in our case by finite points. The higher the point density, the more accurate the simulation is in general, but the larger are the systems of equations that result from the discretization process and have to be solved numerically.
With the simulation accuracy required today, the time in which these equation systems can be solved is a critical variable. Some simulation tasks are very difficult to compute and classic numerical solution methods are not able to solve the resulting large systems of equations in an economically justifiable computing time.

BAMG's solution modules are based on modern hierarchical approaches (algebraic multi-grid methodology, AMG): Instead of just working with the given (extremely large) system of equations, algebraic multi-grid methods combine the numerical information in a hierarchy of increasingly coarse equation systems in order to solve the given problem faster.

Nogrid supports the use of current multi-core computers using OpenMP, while BAMG offers a hybrid MPI/OpenMP approach that applies to any partitioning of the arithmetic grid can apply. The BAMG version makes it possible to use parallel computer architectures to solve the system of equations.

Our new MPI solution enables users to fully utilize the multi-node structure of supercomputing clusters. Message Passing Interface (MPI) is a standard used to allow different nodes on a cluster to communicate with each other. Nogrid uses the Intel Fortran Compiler, GCC, IntelMPI, and OpenMPI to create multiprocessor solver software. Our MPI solution has the following advantages compared to the shared memory model (openMP):

• computation time scales with the number of computers
• runs on either shared or distributed memory architectures
• can be used on a wider range of problems than OpenMP
• each process has its own local variables
• distributed memory computers are less expensive than large shared memory computers

Nogrid models and optimizes industrial applications, develops software and services for product design and process development. In the field of machine learning, Nogrid develops new intelligent methods and adapts data analysis methods to specific user cases. Nogrid takes the knowledge shared by our customers or from the literature, structures it and integrates it into mathematical models. This includes the characterization of properties in structural and fluid mechanics as well as the determination of optimal conditions for e.g. agitators, control tasks or tasks related to shape and design optimization.

All of the optimization problems mentioned are based on the interaction between mathematical analysis and numerical calculations and pose new challenges for both research areas by stimulating and supplementing the development of novel, efficient and computer-aided techniques. The numerical solutions to such optimization problems provide a new understanding of the dynamics of many flows and structures relevant to engineering applications.

In topology optimization, one looks for the design in a given area that is optimal with respect to certain boundary conditions or material properties. A classic example, borrowed from solid mechanics, is shown in Figure 1. Here, an area (upper image) is to be filled 30 percent with material. The question arises as to where to add this material in order for the structure to experience maximum stiffness under the applied load. The result can be seen in the image below and is often referred to as the MBB beam in the literature. Apart from flow systems and solid structures, the topology optimization method can be applied to more or less all areas of engineering, including the design of processes or process steps.