Laboratory of Computational Fluid Dynamics

Department:   Department D 1 - Fluid Dynamics
Head:   RNDr. MgA. Jan Pech, Ph.D.

In the Laboratory of Computational Fluid Dynamics we numerically simulate fluid flows. Our results mostly concern simulations of flows around turbine blades or aerodynamic profiles, heat transfer in flowing fluid and impacts of changes of material properties on flow structures. Various flow regimes require specific approaches to mathematical modelling. This places particular demands on computational methods. The core of our work stays in the development and implementation of such algorithms, however, we also perform simulations related to physical experiments and engineering applications. We develop an in-house code for simulations of turbulent flows based on the finite volume method, we build and implement algorithms for spectral/hp finite elements using the open-source framework Nektar++ and perform advanced finite-volume simulations using OpenFOAM. We also use commercial codes for selected engineering applications. The laboratory cooperates with universities in the Czech Republic (Faculty of Mathematics and Physics of the Charles University, Czech Technical University, Technical University of Liberec) and abroad (Imperial College London, University of Utah).

J. Pech – head of laboratory, specialisation on Spectral/hp finite elements, development of code Nektar++, fluid flow with heat transfer and impact of heating on flow structures

J. Příhoda, P. Louda – development of turbulence models, development of a specialized finite-volume-based in-house code, complex turbomachinery applications

J. Musil – simulation of flows in blade cascades, openFOAM applications


Student positions

D. Jiříček – implementation of turbulence models to the incompressible flow solver in the Nektar++ platform

P. Kosiak – ANSYS applications

The team of the Laboratory of Computational Fluid Dynamics numerically solves problems, the assignment of which usually comes from the experimentally oriented laboratories of the department. This work consists of choosing a suitable mathematical model and an appropriate numerical method. The laboratory brings together experts for specific problems studied in other laboratories.

Computational fluid mechanics is evolving rapidly along with computational technologies. Despite this there is still a wide range of long-term open problems, the most significant of which is the problem of turbulence modelling. Although turbulence is still not fully understood, its manifestations have major implications in technical applications. The Department of Fluid Dynamics has been dealing with this issue since its establishment and at different levels of spatial scales (see other laboratories of the department). Thus, turbulent and transitional phenomena also dominate the simulations conducted by the Laboratory of Computational Fluid Dynamics.

Many of the laboratory's results are directly related to the development of turbulence models (J. Příhoda) and their implementation in the in-house code (P. Louda). Applications then lead to new designs of turbine and compressor blade profiles. The flow velocities in these cases are often comparable with the speed of sound, leading to the emergence of shock waves, as illustrated below, where we compare the image obtained experimentally in the high-speed wind tunnel of the Laboratory of Internal Flows (Fig. 1) and the result of our numerical simulation (On the modelling turbulent transition in turbine cascades with flow separation, Computers and Fluids, 181, 160–172, 2019, ISSN 1003-2169).


Zobrazení rázových vln, které se mohou objevit v proudění v mezilopatkových kanálech konkrétních turbínových strojů. Experimentální výsledek z vysokorychlostního aerodynamického tunelu.

Fig. 1. Shock waves emerging in inter-blade channels of a turbine blade cascade. Physical experiment in high-speed wind tunnel.


Vizualizace proudění jako výsledek numerické simulace stlačitelného proudění z vlastního kódu.Fig. 2. Flow visualization obtained by a numerical simulation of the compressible flow using the in-house code.


The development of turbulence models as well as its implementation to codes based on the finite volume method has a long tradition in the department. The finite volume method has been enjoying a strong support in the Czech scientific community, which also includes other institutes of the Czech Academy of Sciences and universities. Therefore, in addition to the aforementioned in-house code, the members of the laboratory use open-source codes (OpenFOAM), and for fast designs even the commercial package ANSYS. Among the most recent methods, whose ambition is to simulate turbulence up to smallest scales, we should mention the application of the Discontinuous Galerkin method, which is developed and applied in the Laboratory on the platform of another open-source code Nektar++.

For problems solvable by direct simulation, we push the boundaries of the achieved accuracy. This applies in particular to non-stationary fluid flow with heat transfer at lower velocities. A wide spectrum of applications from heat exchangers to detailed studies of flows in the vicinity of measuring probes places high demands especially on the accuracy of the numerical solution. In this area we apply our own scheme for spectral/hp finite elements (Scheme for Evolutionary Navier-Stokes-Fourier System with Temperature Dependent Material Properties Based on Spectral/hp Elements. ICOSAHOM 2018, Lecture Notes in Computational Science and Engineering, vol. 134. Springer).


Fig. 3. Temperature distribution in the flow of fluid, simulation of flow around a heated cylinder (spectral/hp element method with polynomial approximation of degree 50).


Highly accurate results may improve the knowledge of other challenging processes, which can't be fully described experimentally, e.g. the flow separation in the boundary layer of surfaces of bodies in the flow and formation of turbulent structures.


Fig. 4. Detail of flow separation in boundary layer on a curved surface, whose visualization is hardly achievable by current experimental techniques.


In cases where it is possible to apply multiple computational methods, we compare the individual approaches (Comparison of Finite Volume and Spectral/HP Methods on Navier-Stokes Equations for Unsteady Incompressible Flow, Topical Problems of Fluid Mechanics 2018).