Unstructured Finite-volume Flow Solver Research Articles

Fluid-structure interaction of a pulsatile flow with an aortic valve model: A combined experimental and numerical study.

The complex fluid-structure interaction problem associated with the flow of blood through a heart valve with flexible leaflets is investigated both experimentally and numerically. In the experimental test rig, a pulse duplicator generates a pulsatile flow through a biomimetic rigid aortic root where a model of aortic valve with polymer flexible leaflets is implanted. High-speed recordings of the leaflets motion and particle image velocimetry measurements were performed together to investigate the valve kinematics and the dynamics of the flow. Large eddy simulations of the same configuration, based on a variant of the immersed boundary method, are also presented. A massively parallel unstructured finite-volume flow solver is coupled with a finite-element solid mechanics solver to predict the fluid-structure interaction between the unsteady flow and the valve. Detailed analysis of the dynamics of opening and closure of the valve are conducted, showing a good quantitative agreement between the experiment and the simulation regarding the global behavior, in spite of some differences regarding the individual dynamics of the valve leaflets. A multicycle analysis (over more than 20 cycles) enables to characterize the generation of turbulence downstream of the valve, showing similar flow features between the experiment and the simulation. The flow transitions to turbulence after peak systole, when the flow starts to decelerate. Fluctuations are observed in the wake of the valve, with maximum amplitude observed at the commissure side of the aorta. Overall, a very promising experiment-vs-simulation comparison is shown, demonstrating the potential of the numerical method.

Low-Dissipation Low-Dispersion Second-Order Scheme for Unstructured Finite Volume Flow Solvers

A new low-dissipation low-dispersion second-order scheme suitable for unstructured finite volume flow solvers is presented that is designed for vortical flows and for scale-resolving simulations of turbulence. The idea is that, by optimizing its dispersion properties, a standard second-order method can be improved significantly for such flows. The key is to include gradient information for computing face values of the fluxes and to use this additional degree of freedom to improve the dispersion properties of the scheme. The scheme is motivated by a theoretical consideration of the dispersion properties for a one-dimensional scalar transport equation problem. Then, the new scheme is applied using the DLR TAU-code for compressible flows and the DLR THETA-code for incompressible flows for simulations of the moving vortex problem and the Taylor–Green vortex flow. The improved accuracy for small-scale transportation and the easy implementation make this scheme a promising candidate for efficient scale-resolving simulations of turbulent flows.

Validation of an immersed thick boundary method for simulating fluid–structure interactions of deformable membranes

This paper constitutes an extension of the work of Mendez et al. (2014) [36], for three-dimensional simulations of deformable membranes under flow. An immersed thick boundary method is used, combining the immersed boundary method with a three-dimensional modeling of the structural part. The immersed boundary method is adapted to unstructured grids for the fluid resolution, using the reproducing kernel particle method. An unstructured finite-volume flow solver for the incompressible Navier–Stokes equations is coupled with a finite-element solver for the structure. The validation process relying on a number of test cases proves the efficiency of the method, and its robustness is illustrated when computing the dynamics of a tri-leaflet aortic valve. The proposed immersed thick boundary method is able to tackle applications involving both thin and thick membranes/closed and open membranes, in significantly high Reynolds number flows and highly complex geometries.

An unstructured solver for simulations of deformable particles in flows at arbitrary Reynolds numbers

As a step in the development of a numerical procedure able to perform parallel computations of the dynamics of capsules/cells in non-physiological configurations, a numerical method is developed and its validation is described. The fluid–structure interaction problem is solved using an immersed boundary method, adapted to an unstructured finite-volume flow solver thanks to the reproducing kernel particle method. A specific treatment to ensure volume conservation of the fluid enclosed in the immersed structure is also detailed. The present paper focuses on quantitative validation of the method in 2-D, against existing reference 2-D results. Excellent agreement is obtained for configurations of capsules and vesicles evolving with or without mean flow. Applications of the method to non-zero-Reynolds-number cases, including non-trivial geometry, is shown. This unstructured immersed boundary method proves robust to tackle the dynamics of deformable particles in complex flows.

Adaptive Cartesian grid with mesh-less zones for compressible flow calculations

A hybrid grid method that combines the computational efficiency of adaptive Cartesian grids with the flexibility of mesh-less scheme is developed for calculation of compressible flows. The mesh-less zone is created around the geometry by producing layers of nodes along normal direction vectors. Last layer is used as virtual geometry for automatic generation of unstructured Cartesian grid around mesh-less zone. An efficient explicit central difference scheme with artificial dissipation terms and convergence acceleration techniques is developed for both Cartesian grid and mesh-less zones. The method is used for computation of inviscid and viscous flows around single and multi-element airfoils at transonic flow conditions. Results indicate good agreements with those of available unstructured finite-volume flow solver ( Uns2D) and other reference numerical data. The new method is shown to reduce the computational cost up to 70% compared with the fully unstructured flow solver.

A dynamic finite volume scheme for large-eddy simulation on unstructured grids

In recent years there has been considerable progress in the application of large-eddy simulation (LES) to increasingly complex flow configurations. Nevertheless a lot of fundamental problems still need to be solved in order to apply LES in a reliable way to real engineering problems, where typically finite-volume codes on unstructured meshes are used. A self-adaptive discretisation scheme, in the context of an unstructured finite-volume flow solver, is investigated in the case of isotropic turbulence at infinite Reynolds number. The Smagorinsky and dynamic Smagorinsky sub-grid scale models are considered. A discrete interpolation filter is used for the dynamic model. It is one of the first applications of a filter based on the approach presented by Marsden et al. In this work, an original procedure to impose the filter shape through a specific selection process of the basic filters is also proposed. Satisfactory results are obtained using the self-adaptive scheme for implicit LES. When the scheme is coupled with the sub-grid scale models, the numerical dissipation is shown to be dominant over the sub-grid scale component. Nevertheless the effect of the sub-grid scale models appears to be important and beneficial, improving in particular the energy spectra. A test on fully developed channel flow at Re τ = 395 is also performed, comparing the non-limited scheme with the self-adaptive scheme for implicit LES. Once again the introduction of the limiter proves to be beneficial.

The design of improved smoothing operators for finite volume flow solvers on unstructured meshes

Spatial operators used in unstructured finite volume flow solvers are analysed for accuracy using Taylor series expansion and Fourier analysis. While approaching second-order accuracy on very regular grids, operators in common use are shown to have errors resulting in accuracy of only first-, zeroth- or even negative-order on three-dimensional tetrahedral meshes. A technique using least-squares optimization is developed to design improved operators on arbitrary meshes. This is applied to the fourth-order edge sum smoothing operator. The improved numerical dissipation leads to a much more accurate prediction of the Strouhal number for two-dimensional flow around a cylinder and a reduction of a factor of three in the loss coefficient for inviscid flow over a three-dimensional hump. Copyright © 2001 John Wiley & Sons, Ltd.

The design of improved smoothing operators for finite volume flow solvers on unstructured meshes

AbstractSpatial operators used in unstructured finite volume flow solvers are analysed for accuracy using Taylor series expansion and Fourier analysis. While approaching second‐order accuracy on very regular grids, operators in common use are shown to have errors resulting in accuracy of only first‐, zeroth‐ or even negative‐order on three‐dimensional tetrahedral meshes. A technique using least‐squares optimization is developed to design improved operators on arbitrary meshes. This is applied to the fourth‐order edge sum smoothing operator. The improved numerical dissipation leads to a much more accurate prediction of the Strouhal number for two‐dimensional flow around a cylinder and a reduction of a factor of three in the loss coefficient for inviscid flow over a three‐dimensional hump. Copyright © 2001 John Wiley & Sons, Ltd.