Hybridized Implicit-Explicit Flux Reconstruction Methods
CoRR(2024)
摘要
For turbulent problems of industrial scale, computational cost may become
prohibitive due to the stability constraints associated with explicit time
discretization of the underlying conservation laws. On the other hand, implicit
methods allow for larger time-step sizes but require exorbitant computational
resources. Implicit-explicit (IMEX) formulations combine both temporal
approaches, using an explicit method in nonstiff portions of the domain and
implicit in stiff portions. While these methods can be shown to be orders of
magnitude faster than typical explicit discretizations, they are still limited
by their implicit discretization in terms of cost. Hybridization reduces the
scaling of these systems to an effective lower dimension, which allows the
system to be solved at significant speedup factors compared to standard
implicit methods. This work proposes an IMEX scheme that combines hybridized
and standard flux reconstriction (FR) methods to tackle geometry-induced
stiffness. By using the so-called transmission conditions, an overall
conservative formulation can be obtained after combining both explicit FR and
hybridized implicit FR methods. We verify and apply our approach to a series of
numerical examples, including a multi-element airfoil at Reynolds number 1.7
million. Results demonstrate speedup factors of four against standard IMEX
formulations and at least 15 against standard explicit formulations for the
same problem.
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