The scalability and efficiency of numerical methods on parallel computer architectures is of prime importance as we march towards exascale computing. Classical methods like finite difference schemes and finite volume methods have inherent roadblocks in their mathematical construction to achieve good scalability. These methods are popularly used to solve the Navier-Stokes equations for fluid flow simulations. The discontinuous Galerkin family of methods for solving continuum partial differential equations has shown promise in realizing parallel efficiency and scalability when approaching petascale computations. In this paper an explicit modal discontinuous Galerkin (DG) method utilizing Implicit Large Eddy Simulation (ILES) is proposed for unsteady turbulent flow simulations involving the three-dimensional Navier-Stokes equations. A study of the method was performed for the Taylor-Green vortex case at a Reynolds number ranging from 100 to 1600. The polynomial order
Optimal estimates on stabilized finite volume methods for the three dimensional Navier–Stokes model are investigated and developed in this paper. Based on the global existence theorem [23], we first prove the global bound for the velocity in the
- PAR ID:
- 10075717
- Publisher / Repository:
- Wiley Blackwell (John Wiley & Sons)
- Date Published:
- Journal Name:
- Numerical Methods for Partial Differential Equations
- Volume:
- 35
- Issue:
- 1
- ISSN:
- 0749-159X
- Page Range / eLocation ID:
- p. 128-154
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Abstract P = 2 (third order accurate) was found to closely match the Direct Navier-Stokes (DNS) results for all Reynolds numbers tested outside of Re = 1600, which had a normalized RMS error of 3.43 × 10−4in the dissipation rate for a 603element mesh. The scalability and performance study of the method was then conducted for a Reynolds number of 1600 for polynomials orders fromP = 2 toP = 6. The highest order polynomial that was tested (P = 6) was found to have the most efficient scalability using both the MPI and OpenMP implementations. -
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Summary A new approach has been developed for combining and enhancing the results from an existing computational fluid dynamics model with experimental data using the weighted least‐squares finite element method (WLSFEM). Development of the approach was motivated by the existence of both limited experimental blood velocity in the left ventricle and inexact numerical models of the same flow. Limitations of the experimental data include measurement noise and having data only along a two‐dimensional plane. Most numerical modeling approaches do not provide the flexibility to assimilate noisy experimental data. We previously developed an approach that could assimilate experimental data into the process of numerically solving the Navier–Stokes equations, but the approach was limited because it required the use of specific finite element methods for solving all model equations and did not support alternative numerical approximation methods. The new approach presented here allows virtually any numerical method to be used for approximately solving the Navier–Stokes equations, and then the WLSFEM is used to combine the experimental data with the numerical solution of the model equations in a final step. The approach dynamically adjusts the influence of the experimental data on the numerical solution so that more accurate data are more closely matched by the final solution and less accurate data are not closely matched. The new approach is demonstrated on different test problems and provides significantly reduced computational costs compared with many previous methods for data assimilation. Copyright © 2016 John Wiley & Sons, Ltd.
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