Multiphase flow simulations
Many physical situations, e.g., oil droplets in water, or blood cells in blood plasma, can be modeled as a mixture of two immiscible, incompressible fluids with an interface between the fluids. Such problems are typically modelled by the incompressible Navier-Stokes equations, which describe the fluid flow, coupled with a model for the evolution of the interface between the fluids. One example of such a model is the level set method, where the interface is tracked implicitly via a scalar level set field. The location of the interface is determined by the zero contour of the level set field. The scalar level set field, and thus also the interface, is moved according to the local fluid velocity.
Using the finite element method to discretize the resulting system of partial differential equations allows for flexibility with respect to the geometry and adaptive mesh refinement. In order to accurately simulate realistic problems in 3D, millions or even billions of degrees of freedom can be required. In this case, efficient parallel implementations for large-scale computer systems are necessary.
In this project we are using and actively developing the open-source finite element C++ library deal.II.
Models for contact lines
Problems involving two fluids that are in contact with a solid are called moving contact line problems (or contact point problems, in 2D). For these problems the standard model is not accurate: by the no-slip boundary condition, appropriate for Navier-Stokes equations describing the fluid velocities, the contact line cannot move. This is not true in reality (think of rain drops flowing down a window). Therefore, in simulations of moving contact line problems it is necessary to introduce slip at the boundary representing the solid. However, introducing slip in an accurate way is not straightforward. Common problems are inaccuracies in the model and grid effects.
One idea how to introduce slip is based on the so-called hydrodynamic model for steady movement of a contact line. The hydrodynamic model consists of an analytical expression for the fluid velocity field close to a moving contact line. The velocity field from the hydrodynamic model can then be used to impose a slip boundary condition at the solid and in this way move the contact line.
Parallel implementations for CPUs and GPUs
We also develop methods for efficient utilization of modern computer hardware.
The majority of the computational work in a multiphase flow simulation consists of matrix-vector products inside an iterative linear solver. However, with its low computational intensity, the sparse matrix-vector product is very poorly suited for the architecture of modern multi-core processors, where data transfer is expensive and computations are cheap. This issue grows with the number of unknowns and becomes especially severe when high-order basis functions in 3D are used.
Matrix-free methods based on tensor products do not rely on an explicit matrix for performing the matrix-vector products, but merely knows the recipe for performing the product. This introduces additional computations, since the contribution of the matrix will have to be calculated upon each product, but greatly reduces the amount of data transfer, and is thus much better adapted to present and future hardware.
Recently, graphics processors (GPUs) have seen an increasing use for computations in science and engineering, since they offer lots of computational power cheaply, both in terms of power consumption and price. The high computational intensity of the matrix-free method makes it well suited for execution on graphics processors, which even more than regular processors are optimized for compute-intensive tasks.
Application: microfluidic device for cell sorting
Nowadays microfluidics technology allows for successful control of the fluidic environment at the scale of cells. In this work we are dealing with a microfluidic chip that enables high-throughput separation of bacteria from human bloods cells. The flow in these chips is characterized by low Reynolds numbers, i.e., a laminar flow behavior, which is why single cell handling and analysis is possible. Our aim is to numerically demonstrate the ability of the device to sort not only differently sized particles but to also sort particles of different densities. Here we are faced with the motion of binary fluids that includes two phases of different composition. This dynamical system can be modeled by the two-phase flow equations.
- Matrix-free finite-element operator application on graphics processing units. In Euro-Par 2014: Parallel Processing Workshops, Part II, volume 8806 of Lecture Notes in Computer Science, pp 450-461, Springer, 2014. (DOI).
- Massively parallel finite element programming. In Recent Advances in the Message Passing Interface, volume 6305 of Lecture Notes in Computer Science, pp 122-131, Springer-Verlag, Berlin, 2010. (DOI).
- A conservative level set method for contact line dynamics. In Journal of Computational Physics, volume 228, pp 6361-6375, 2009. (DOI).
- A hybrid level-set Cahn–Hilliard model for two-phase flow. In Proc. 1st European Conference on Microfluidics, pp 59:1-10, La Société Hydrotechnique de France, 2008. (fulltext:postprint).
- An interface capturing method for two-phase flow with moving contact lines. In Proc. 1st European Conference on Microfluidics, pp 118:1-10, La Société Hydrotechnique de France, 2008. (fulltext:postprint).
- A conservative level set method for two phase flow II. In Journal of Computational Physics, volume 225, pp 785-807, 2007. (DOI).
- A conservative level set method for two phase flow. Elin Olsson and Gunilla Kreiss. In Journal of Computational Physics, volume 210, pp 225-246, 2005.
- Towards accurate modeling of moving contact lines. Licentiate thesis, IT licentiate theses / Uppsala University, Department of Information Technology nr 2015-006, Uppsala University, 2015. (fulltext).
- Techniques for finite element methods on modern processors. Licentiate thesis, IT licentiate theses / Uppsala University, Department of Information Technology nr 2015-001, Uppsala University, 2015. (fulltext).
- Computational Techniques for Coupled Flow-Transport Problems. Ph.D. thesis, Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology nr 885, Acta Universitatis Upsaliensis, Uppsala, 2011. (fulltext).
- Numerical Modeling of Fluid Interface Phenomena. Sara Zahedi. Licentiate thesis, Trita-CSC-A / Royal Institute of Technology, Department of Numerical Analysis and Computing Science nr 2009:7, 2009.
- Mass conserving simulations of two phase flow. Elin Olsson. Licentiate thesis, Trita-NA / Royal Institute of Technology, Department of Numerical Analysis and Computing Science nr 0556, 2006.
Contact: , Gunilla Kreiss