A implicit, discontinuous Galerkin Chimera solver using automatic differentiation

Wukie, Nathan A.; Orkwis, Paul D.

doi:10.2514/6.2016-2054

Cited by 10 publications

(2 citation statements)

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“…14 In this way, as the spatial residual converges to zero, the time-step increases to infinity and the original full Newton method is recovered. The general method for computing the linearization utilizes an automatic differentiation technique that was detailed previously by Wukie et al 4 The linearization for fully-coupled boundary conditions is discussed later in the present work. Solving for ∆Q, the solution is updated as…”

Section: Iib Nonlinear Solvermentioning

confidence: 99%

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A fully-implicit, Giles-type nonreflecting boundary condition in a DG-Chimera turbomachinery solver

Wukie

Orkwis

Turner

2016

46th AIAA Fluid Dynamics Conference

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Development of a fully-implicit, Giles-type nonreflecting boundary condition in a computational fluid dynamics solver using a discontinuous Galerkin method on Chimera overset grids is demonstrated. The implicit formulation is in the context of Newton's method. The implementation was completed without the use of ghost elements or extra degrees of freedom in the system of equations and the boundary condition is not lagged. Rather, the elements associated with the nonreflecting boundary are fully-coupled with each other in the Newton linearization. The linearization of the governing equations and boundary conditions is achieved via an automatic differentiation technique based on operator overloading. Calculations of a turbine cascade geometry using truncated and extended domains were computed. Comparison of pressure and flow angles at the exit plane location between the truncated and extended domains were very well matched. All calculations converged in 4-7 Newton iterations up through 4 th -order accuracy.

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Section: Iib Nonlinear Solvermentioning

confidence: 99%

“…4 The framework was implemented with an intrinsic automatic differentiation capability which greatly reduces the effort required to implement new equation sets and boundary conditions while still maintaining Newton convergence of the implicit scheme.…”

Section: Ia Implicit Dg-chimera Frameworkmentioning

confidence: 99%