Applying High-Order, Adaptively-Refined, Finite-Volume Methods to Discrete Structured Representations of Arbitrary Geometry

Overton‐Katz, Nathaniel; Gao, Xinfeng; Guzik, Stephen M.

doi:10.2514/6.2020-1310

Cited by 1 publication

(3 citation statements)

References 9 publications

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“…⟩ the solution at the ith stage, and L [𝜈],(i) = L(⟨JU (i) ⟩) [𝜈] the additive term 𝜈. A nonlinear problem arises from Equation (17), for which the specifics of solving depend on the exact ARK method employed. At the end of the mth stage, the solution is updated with…”

Section: Fourth-order Imex Ark Methodsmentioning

confidence: 99%

“…The superscript [ns] indicates the nonstiff term that is solved explicitly and the superscript [s] indicates the stiff term that is solved implicitly. Substitute these two terms into Equation (17) to get the specific stage values…”

Section: Fourth-order Imex Ark Methodsmentioning

confidence: 99%

“…The system of PDEs governing compressible combustion consists of the Navier-Stokes and a set of species transport equations 3,13 and specifically the mapped version 14,15 is used for this study. Furthermore, we employ mapped multiblock techniques 16,17 to represent complicated geometry on a Cartesian grid with AMR. To provide a brief background, the system of equations is given here.…”

Section: Mathematical Modelingmentioning

confidence: 99%

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High‐order implicit‐explicit additive Runge–Kutta schemes for numerical combustion with adaptive mesh refinement

Christopher

Guzik

Gao

2022

Numerical Methods in Fluids

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The objective of this study is to develop and apply efficient solution techniques for numerical modeling of combustion with stiff chemical kinetics in practical combustors. The new technique combines a fourth-order implicit-explicit (IMEX) additive Runge-Kutta scheme (ARK) with adaptive mesh refinement (AMR). The IMEX component treats the stiff reactions implicitly but integrates convection and diffusion explicitly in time, and thus permits the solution to advance with larger time-step sizes than that of explicit time-marching methods alone. The AMR further adds computational efficiency by effectively placing high spatial resolution meshes in regions with strong gradients, such as flame fronts. The novelty of this study is in the integration of a fourth-order IMEX ARK method with AMR for a high-order finite-volume scheme and the application to solving complex reacting flows governed by the compressible Navier-Stokes equations with very stiff chemistry in a practical combustor geometry. The effectiveness and performance of the adaptive ARK4 is assessed for complex reacting flows by examining properties, such as the presence of shock waves, the time-scale changes in response to AMR levels, and the size and stiffness of reaction mechanisms for various fuels such as H 2 , CH 4 , and C 3 H 8 . The new adaptive ARK4 method is verified and validated using a convection-diffusion-reaction problem and shock-driven combustion, respectively. The validated algorithm is then applied to solve the stiff C 3 H 8 -air combustion in a bluff-body combustor. A significant speedup of three orders of magnitude is achieved in comparison to the standard ERK4 method at the given solution accuracy.

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Section: Fourth-order Imex Ark Methodsmentioning

confidence: 99%

Section: Fourth-order Imex Ark Methodsmentioning

confidence: 99%