A parallel, high-order discontinuous Galerkin code for laminar and turbulent flows. (English) Zbl 1237.76071
Summary: In this study we present a solution method for the compressible Navier-Stokes equations as well as the Reynolds-averaged Navier-Stokes equations (RANS) based on a discontinuous Galerkin (DG) space discretisation. For the turbulent computations we use the standard Wilcox \(k-\omega\) or the Spalart- Allmaras model in order to close the RANS system. We currently apply either a local discontinuous Galerkin (LDG) or one of the Bassi-Rebay formulations (BR2) for the discretisation of second-order viscous terms. Both approaches (LDG and BR2) can be advanced explicitly as well as implicitly in time by classical integration methods. The boundary is approximated in a continuously differentiable fashion by curved elements not to spoil the high-order of accuracy in the interior of the flow field.
MSC:
| 76M10 | Finite element methods applied to problems in fluid mechanics |
| 76F60 | \(k\)-\(\varepsilon\) modeling in turbulence |
References:
| [1] | Spalart PR, Jou W-H, Strelets M, Allmaras S. Comments on the feasibility of LES for wings, and on a hybrid RANS/LES approach. In: Advances in DNS/LES; 1997.; Spalart PR, Jou W-H, Strelets M, Allmaras S. Comments on the feasibility of LES for wings, and on a hybrid RANS/LES approach. In: Advances in DNS/LES; 1997. |
| [2] | Sagaut, P., Large eddy simulation for incompressible flows (2002), Springer · Zbl 1020.76001 |
| [3] | van der Vegt, J.; van der Ven, H., Space-time discontinuous Galerkin finite element method with dynamic grid motion for inviscid compressible flows. Part I. General formulation, J Comput Phys, 182, 546-585 (2002) · Zbl 1057.76553 |
| [4] | Cockburn, B.; Shu, C., The Runge-Kutta discontinuous Galerkin finite element method for conservation laws v: multidimensional systems, J Comput Phys, 141, 199-224 (1998) · Zbl 0920.65059 |
| [5] | Bassi, F.; Rebay, S., High-order accurate discontinuous finite element solution of the 2D Euler equations, J Comput Phys, 138, 251-285 (1997) · Zbl 0902.76056 |
| [6] | Bassi, F.; Rebay, S., A high-order discontinuous Galerkin method for compressible turbulent flows, (Cockburn, B.; Karniadakis, G. E.; Shu, C.-W., Discontinuous Galerkin methods (2000), Springer), 77-88 · Zbl 0991.76039 |
| [7] | Bassi, F.; Rebay, S., Discontinuous Galerkin solution of the Reynolds-averaged Navier-Stokes and \(k-ω\) turbulence model equations, J Comput Fluids, 34, 507-540 (2005) · Zbl 1138.76043 |
| [8] | Wilcox, D., Turbulence modeling for CFD (1998), DCW Industries: DCW Industries La Canada |
| [9] | Spalart P, Allmaras S. A one-equation turbulence model for aerodynamic flows, Tech Rep, AIAA-92-0439; 1992.; Spalart P, Allmaras S. A one-equation turbulence model for aerodynamic flows, Tech Rep, AIAA-92-0439; 1992. |
| [10] | Harten, A.; Lax, P.; van Leer, B., On upstream differencing and Godunov-type schemes for hyperbolic conservation laws, SIAM Rev, 25, 35-61 (1983) · Zbl 0565.65051 |
| [11] | Roe, P., Approximate riemann solvers, parameter vectors and difference schemes, J Comput Phys, 43, 357-372 (1981) · Zbl 0474.65066 |
| [12] | Cockburn, B.; Shu, C.-W., The local discontinuous Galerkin method for time-dependent convection-diffusion systems, SIAM J Numer Anal, 35, 2440-2463 (1998) · Zbl 0927.65118 |
| [13] | Wilcox, D., Reassessment of the scale-determining equation for advanced turbulence models, AIAA J, 26, 11, 1299-1310 (1988) · Zbl 0664.76057 |
| [14] | Oliver T. Multigrid solution for high-order discontinuous Galerkin discretizations of the compressible Navier-Stokes equations. Master’s Thesis, MIT, Department of Aeronautics and Astronautics; 2004.; Oliver T. Multigrid solution for high-order discontinuous Galerkin discretizations of the compressible Navier-Stokes equations. Master’s Thesis, MIT, Department of Aeronautics and Astronautics; 2004. |
| [15] | Inoue, O.; Hatakeyama, N., Sound generation by a two-dimensional circular cylinder in a uniform flow, J Fluid Mech, 471, 285-314 (2002) · Zbl 1026.76045 |
| [16] | Williamson, C., Oblique and parallel modes of vortex shedding in the wake of a circular cylinder at low reynolds numbers, J Fluid Mech, 206, 579-627 (1989) |
| [17] | Haase, W.; Chaput, E.; Elsholz, E.; Leschziner, M.; Müller, U., ECARP - European computational aerodynamics research project: validation of CFD codes and assessment of turbulence models. ECARP - European computational aerodynamics research project: validation of CFD codes and assessment of turbulence models, Notes on numerical fluid mechanics, vol. 58 (1997), Viehweg |
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
