482 research outputs found
Assessment of high-order IMEX methods for incompressible flow
This paper investigates the competitiveness of semi-implicit Runge-Kutta (RK)
and spectral deferred correction (SDC) time-integration methods up to order six
for incompressible Navier-Stokes problems in conjunction with a high-order
discontinuous Galerkin method for space discretization. It is proposed to
harness the implicit and explicit RK parts as a partitioned scheme, which
provides a natural basis for the underlying projection scheme and yields a
straight-forward approach for accommodating nonlinear viscosity. Numerical
experiments on laminar flow, variable viscosity and transition to turbulence
are carried out to assess accuracy, convergence and computational efficiency.
Although the methods of order 3 or higher are susceptible to order reduction
due to time-dependent boundary conditions, two third-order RK methods are
identified that perform well in all test cases and clearly surpass all
second-order schemes including the popular extrapolated backward difference
method. The considered SDC methods are more accurate than the RK methods, but
become competitive only for relative errors smaller than ca
Computational fluid dynamics for aerospace propulsion systems: an approach based on discontinuous finite elements
The purpose of this work is the development of a numerical tool devoted to the
study of the flow field in the components of aerospace propulsion systems. The
goal is to obtain a code which can efficiently deal with both steady and unsteady
problems, even in the presence of complex geometries.
Several physical models have been implemented and tested, starting from Euler
equations up to a three equations RANS model. Numerical results have been compared
with experimental data for several real life applications in order to understand
the range of applicability of the code. Performance optimization has been
considered with particular care thanks to the participation to two international
Workshops in which the results were compared with other groups from all over the
world.
As far as the numerical aspect is concerned, state-of-art algorithms have been implemented
in order to make the tool competitive with respect to existing softwares.
The features of the chosen discretization have been exploited to develop adaptive
algorithms (p, h and hp adaptivity) which can automatically refine the discretization.
Furthermore, two new algorithms have been developed during the research
activity. In particular, a new technique (Feedback filtering [1]) for shock capturing
in the framework of Discontinuous Galerkin methods has been introduced. It is
based on an adaptive filter and can be efficiently used with explicit time integration
schemes. Furthermore, a new method (Enhance Stability Recovery [2]) for
the computation of diffusive fluxes in Discontinuous Galerkin discretizations has
been developed. It derives from the original recovery approach proposed by van
Leer and Nomura [3] in 2005 but it uses a different recovery basis and a different
approach for the imposition of Dirichlet boundary conditions. The performed numerical
comparisons showed that the ESR method has a larger stability limit in
explicit time integration with respect to other existing methods (BR2 [4] and original
recovery [3]). In conclusion, several well known test cases were studied in order
to evaluate the behavior of the implemented physical models and the performance
of the developed numerical schemes
A high order accurate bound-preserving compact finite difference scheme for scalar convection diffusion equations
We show that the classical fourth order accurate compact finite difference
scheme with high order strong stability preserving time discretizations for
convection diffusion problems satisfies a weak monotonicity property, which
implies that a simple limiter can enforce the bound-preserving property without
losing conservation and high order accuracy. Higher order accurate compact
finite difference schemes satisfying the weak monotonicity will also be
discussed
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