Computational Mechanics and Numerical Mathematics > Math > JBI > FWN > RUG


With the continuing progress in numerical mathematics and computer technology, the impact of computer simulation on society is rapidly increasing. Our group specializes in numerical algorithms for the simulation of fluid dynamics and transport phenomena (Computational Fluid Dynamics CFD). On the one hand research is focussed on basic advancement of numerical algorithms; on the other hand - through extensive cooperation with external research groups - these methods are made available to advance knowledge in other (applied) areas of science and technology.

Turbulent flow

Fluid flow simulations use turbulence models for the small details that cannot be resolved numerically. This keeps the computational effort within reasonable limits, but a price is paid in terms of accuracy. To improve the accuracy, we perform research into large-eddy simulation (LES) and direct numerical simulation (DNS). The mathematical rationale behind our approach focusses on approximations that preserve the underlying PDE structure as well as on regularizations that truncate the nonlinear interactions with small scales of motions.

Free-surface flow and fluid-structure interaction

The main free-surface flow research concerns application in maritime and coastal engineering. Numerical simulation methods are developed to predict hydrodynamic wave loading on moving and/or deforming offshore platforms (fluid-structure interaction) and coastal structures. The basic tool is the in-house developed simulation method ComFLOW. Our bio-medical fluid dynamics applications fit in the area of fluid-structure interaction. In cooperation with UMCG we study arterial blood flow in elastic vessels and its influence on atherosclerosis. Also the mechanics of the human ear (cochlea) has our attention.

Sparse-matrix solvers

The repeated solution of large systems of equations in most simulation methods makes the quest for improved matrix solvers another major research area. In-house a number of multilevel preconditoners have been developed. For general systems, we designed MRILU (Matrix renumbering ILU) and VBARMS (Variable Block Algebraic Recursive Multilevel Solver). MRILU can be applied to discretizations of coupled PDEs. It particularly performs well for convection-diffusion equations. VBARMS almost automatically exploits any available block structure during the factorization, achieving increased throughput during the computation and improved reliability on realistic applications. Both VBARMS and HYMLS are parallelized using MPI. Additionally, the special purpose multilevel preconditioner HYMLS (Hybrid Multilevel solver) is designed to meet the incompressiblity constraint efficiently. Typical application areas of the solvers are fluid flow, structural problems, electro magnetics and bifurcation analysis.

Bifurcation analysis Here the emphasis is on numerical methods for investigating the bifurcation behaviour of fluid flow, from academic to real world problems like the global ocean circulation. Recently we started the development of methods to study the influence of noise on stability and bifurcation.

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