## Finite element computation of turbulent flows with the discontinuity-capturing directional dissipation (DCDD).(English)Zbl 1181.76098

Summary: The streamline-upwind/Petrov–Galerkin (SUPG) and pressure-stabilizing/Petrov–Galerkin (PSPG) methods are among the most popular stabilized formulations in finite element computation of flow problems. The discontinuity-capturing directional dissipation (DCDD) was first introduced as a complement to the SUPG and PSPG stabilizations for the computation of incompressible flows in the presence of sharp solution gradients. The DCDD stabilization takes effect where there is a sharp gradient in the velocity field and introduces dissipation in the direction of that gradient. The length scale used in defining the DCDD stabilization is based on the solution gradient. Here we describe how the DCDD stabilization, in combination with the SUPG and PSPG stabilizations, can be applied to computation of turbulent flows. We examine the similarity between the DCDD stabilization and a purely dissipative energy cascade model. To evaluate the performance of the DCDD stabilization, we compute as test problem a plane channel flow at friction Reynolds number $$Re_{\tau } = 180$$.

### MSC:

 76M10 Finite element methods applied to problems in fluid mechanics 76F99 Turbulence
Full Text:

### References:

 [1] Sagaut, P., Large eddy simulation for incompressible flows—an introduction, (1998), Springer-Verlag New York [2] Dubois, T.; Jauberteau, F.; Temam, R., Solution of the incompressible navier – stokes equations by the nonlinear Galerkin method, J sci comput, 8, 167-194, (1993) · Zbl 0783.76068 [3] Hughes, T.J.R., Multiscale phenomena: green’s functions, the Dirichlet-to-Neumann formulation, subgrid scale models, bubbles, and the origins of stabilized methods, Comput methods appl mech eng, 127, 387-401, (1995) · Zbl 0866.76044 [4] Hughes, T.J.R.; Mazzei, L.; Jansen, K.E., Large eddy simulation and the variational multiscale method, Comput visual sci, 3, 47-59, (2000) · Zbl 0998.76040 [5] Hughes, T.J.R.; Mazzei, L.; Oberai, A.A.; Wray, A.A., The multiscale formulation of large eddy simulation: decay of homogeneous isotropic turbulence, Phys fluids, 13, 505-512, (2001) · Zbl 1184.76236 [6] Jansen, K.E., A stabilized finite element method for computing turbulence, Comput methods appl mech eng, 174, 299-317, (1999) · Zbl 0958.76041 [7] Hughes, T.J.R.; Brooks, A.N., A multi-dimensional upwind scheme with no crosswind diffusion, (), 19-35 · Zbl 0423.76067 [8] Brooks, A.N.; Hughes, T.J.R., Streamline upwind/petrov – galerkin formulations for convection dominated flows with particular emphasis on the incompressible navier – stokes equations, Comput methods appl mech eng, 32, 199-259, (1982) · Zbl 0497.76041 [9] Tezduyar TE, Hughes TJR. Finite element formulations for convection dominated flows with particular emphasis on the compressible Euler equations. In: Proceedings of AIAA 21st Aerospace Sciences Meeting, AIAA Paper 83-0125. Reno, Nevada: 1983. [10] Hughes, T.J.R.; Tezduyar, T.E., Finite element methods for first-order hyperbolic systems with particular emphasis on the compressible Euler equations, Comput methods appl mech eng, 45, 217-284, (1984) · Zbl 0542.76093 [11] Tezduyar, T.E., Stabilized finite element formulations for incompressible flow computations, Adv appl mech, 28, 1-44, (1992) · Zbl 0747.76069 [12] Tezduyar, T.E.; Park, Y.J., Discontinuity capturing finite element formulations for nonlinear convection – diffusion – reaction equations, Comput methods appl mech eng, 59, 307-325, (1986) · Zbl 0593.76096 [13] Hughes, T.J.R.; Franca, L.P.; Balestra, M., A new finite element formulation for computational fluid dynamics: V. circumventing the babuška – brezzi condition: A stable petrov – galerkin formulation of the Stokes problem accommodating equal-order interpolations, Comput methods appl mech eng, 59, 85-99, (1986) · Zbl 0622.76077 [14] Tezduyar, T.E.; Osawa, Y., Finite element stabilization parameters computed from element matrices and vectors, Comput methods appl mech eng, 190, 411-430, (2000) · Zbl 0973.76057 [15] Tezduyar, T.E., Computation of moving boundaries and interfaces and stabilization parameters, Int J numer methods fluids, 43, 555-575, (2003) · Zbl 1032.76605 [16] Tezduyar, T.; Sathe, S., Stabilization parameters in SUPG and PSPG formulations, J comput appl mech, 4, 71-88, (2003) · Zbl 1026.76032 [17] Tezduyar, T.E., Finite element methods for fluid dynamics with moving boundaries and interfaces, (), [Chapter 17] · Zbl 0848.76036 [18] Tezduyar TE. Adaptive determination of the finite element stabilization parameters. In: Proceedings of the ECCOMAS Computational Fluid Dynamics Conference 2001 (CD-ROM). Swansea, Wales, United Kingdom: 2001. [19] Leonard, B.P., A stable and accurate convective modeling procedure based on quadratic upstream interpolation, Comput methods appl mech eng, 19, 59-98, (1979) · Zbl 0423.76070 [20] Kawamura T, Kuwahara K. Computation of high reynolds number flow around a circular cylinder with surface roughness. In: AIAA 22nd Aerospace Sciences Meeting. Reno, Nevada: 1984. [21] Engquist, B.; Lotstedt, P.; Sjogreen, B., Nonlinear filter for efficient shock computation, Math comput, 52, 509-536, (1989) · Zbl 0667.65073 [22] Borello D, Borrelli P, Quagliata E, Rispoli F. A multi-grid additive and distributive parallel algorithm for finite element turbomachinery CFD. In: Proceedings of the ECCOMAS Computational Fluid Dynamics Conference 2001 (CD-ROM). Swansea, Wales, United Kingdom: 2001. [23] Borello, D.; Corsini, A.; Rispoli, F., A finite element overlapping scheme for turbomachinery flows on parallel platforms, Comput fluids, 32/7, 1017-1047, (2003) · Zbl 1137.76410 [24] Rispoli F, Borrelli P,Tezduyar TE. Discontinuity-capturing directional dissipation (DCDD) in computation of turbulent flows. In: Proceedings of the European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2004 (CD-ROM). Jyvaskyla, Finland: 2004. [25] Rispoli F, Borrelli P, Tezduyar TE. Computation of turbulent flows with the discontinuity-capturing directional dissipation DCDD. In: Proceedings of the 6th World Congress on Computational Mechanics (CD-ROM). Beijing, China: 2004. [26] Rispoli, F.; Borrelli, P.; Tezduyar, T.E., DCDD in finite element computation of turbulent flows, () [27] Kim, J.; Moin, P.; Moser, R., Turbulence statistics in fully developed channel flow at low Reynolds number, J fluid mech, 177, 133-166, (1987) · Zbl 0616.76071 [28] Dean, R.B., Reynolds number dependence of skin friction and other bulk flow variables in two-dimensional rectangular duct flow, J fluids eng, 10, 215-223, (1978)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.