539 research outputs found
A spectral deferred correction strategy for low Mach number reacting flows subject to electric fields
We propose an algorithm for low Mach number reacting flows subjected to
electric field that includes the chemical production and transport of charged
species. This work is an extension of a multi-implicit spectral deferred
correction (MISDC) algorithm designed to advance the conservation equations in
time at scales associated with advective transport. The fast and nontrivial
interactions of electrons with the electric field are treated implicitly using
a Jacobian-Free Newton Krylov approach for which a preconditioning strategy is
developed. Within the MISDC framework, this enables a close and stable coupling
of diffusion, reactions and dielectric relaxation terms with advective
transport and is shown to exhibit second-order convergence in space and time.
The algorithm is then applied to a series of steady and unsteady problems to
demonstrate its capability and stability. Although developed in a
one-dimensional case, the algorithmic ingredients are carefully designed to be
amenable to multidimensional applications
A Jacobian-free Newton-Krylov method for time-implicit multidimensional hydrodynamics
This work is a continuation of our efforts to develop an efficient implicit
solver for multidimensional hydrodynamics for the purpose of studying important
physical processes in stellar interiors, such as turbulent convection and
overshooting. We present an implicit solver that results from the combination
of a Jacobian-Free Newton-Krylov method and a preconditioning technique
tailored to the inviscid, compressible equations of stellar hydrodynamics. We
assess the accuracy and performance of the solver for both 2D and 3D problems
for Mach numbers down to . Although our applications concern flows in
stellar interiors, the method can be applied to general advection and/or
diffusion-dominated flows. The method presented in this paper opens up new
avenues in 3D modeling of realistic stellar interiors allowing the study of
important problems in stellar structure and evolution.Comment: Accepted for publication in A&
Multilevel Variable-Block Schur-Complement-Based Preconditioning for the Implicit Solution of the Reynolds- Averaged Navier-Stokes Equations Using Unstructured Grids
Implicit methods based on the Newton’s rootfinding algorithm are receiving an increasing attention for the solution of complex Computational Fluid Dynamics (CFD) applications due to their potential to converge in a very small number of iterations. This approach requires fast convergence acceleration techniques in order to compete with other conventional solvers, such as those based on artificial dissipation or upwind schemes, in terms of CPU time. In this chapter, we describe a multilevel variable-block Schur-complement-based preconditioning for the implicit solution of the Reynolds-averaged Navier-Stokes equations using unstructured grids on distributed-memory parallel computers. The proposed solver detects automatically exact or approximate dense structures in the linear system arising from the discretization, and exploits this information to enhance the robustness and improve the scalability of the block factorization. A complete study of the numerical and parallel performance of the solver is presented for the analysis of turbulent Navier-Stokes equations on a suite of three-dimensional test cases
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