DNS 1-3 Computational Details
Computational Details
Computational approach
Alya is a parallel multi-physics/multiscale simulation code developed at the Barcelona Supercomputing Centre to run efficiently on high-performance computing environments. The convective term is discretized using a Galerkin finite element (FEM) scheme recently proposed in Charnyi et al. (2017) and Jofre et al. (2014), which conserves linear and angular momentum, and kinetic energy at the discrete level. Both second- and third-order spatial discretizations are used.
Neither upwinding nor any equivalent momentum stabilization is employed. In order to use equalorder elements, numerical dissipation is introduced only for the pressure stabilization via a fractional step scheme Codina (2017), which is similar to approaches for pressure-velocity coupling in unstructured, collocated finite-volume codes Jofre et al. (2014). The set of equations is integrated in time using a third order Runge-Kutta explicit method combined with an eigenvalue-based time-step estimator [14]. This approach has been shown to be significantly less dissipative than the traditional stabilized FEM approach [15]. Thus, is an optimal methodology for high-fidelity simulations of complex flows as the ones required in the present project.
Spatial and temporal resolution, grids
A mesh resulting in approximately 250 million degrees of freedom (DoF). With a stretched grid, the maximum grid resolution in the duct centre is reported at Δz + = 11.6, Δy + = 13.2 and Δx += 19.5. Correspondingly, the wall resolution (in terms of the first grid point) is reported as z += 0.074, y + = 0.37 in the spanwise and normal directions, respectively, is used. This resolution was deemed sufficient to compute the flow in the diffuser and is based on the previous work of Ohlsson et al. (2010). For the temporal resolution a third order explicit Runge Kutta method using a dynamic time stepping with CFL below 0.9 has been used.
Computation of statistical quantities
Describe how the averages and correlations are obtained from the instantaneous results and how terms in the budget equations are computed, in particular if there are differences to the proposed approach in Introduction.
References
- Charnyi, S., Heister, T., Olshanskii, M. A. and Rebholz, L. G. (2017): On conservation laws of NavierStokes Galerkin discretizations. In Journal of Computational Physics, Vol. 337, pp. 289-308.
- Jofre, L., Lehmkuhl, O., Ventosa, J., Trias, F. and Oliva, A. (2014): Conservation properties of unstructured finite-volume mesh schemes for the Navier-Stokes equations. In Numerical Heat Transfer, Part B: Fundamentals, Vol. 54, no. 1, pp. 289-308.
- Codina, R. (2001): Pressure stability in fractional step finite element methods for incompressible flows. In Journal of Computational Physics, Vol. 170, no. 1, pp. 112-140.
Contributed by: Oriol Lehmkuhl, Arnau Miro — Barcelona Supercomputing Center (BSC)
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