A freestream-preserving fourth-order finite-volume method in mapped coordinates with adaptive-mesh refinement

Owen

Guzik

2016

SUMMARYA fourth-order finite-volume method for solving the Navier-Stokes equations on a mapped grid with adaptive mesh refinement is proposed, implemented, and demonstrated for the prediction of unsteady compressible viscous flows. The method employs fourth-order quadrature rules for evaluating face-averaged fluxes. Our approach is freestream preserving, guaranteed by the way of computing the averages of the metric terms on the faces of cells. The standard Runge-Kutta marching method is used for time discretization. Solutions of a smooth flow are obtained in order to verify that the method is formally fourth-order accurate when applying the nonlinear viscous operators on mapped grids. Solutions of a shock tube problem are obtained to demonstrate the effectiveness of adaptive mesh refinement in resolving discontinuities. A Mach reflection problem is solved to demonstrate the mapped algorithm on a non-rectangular physical domain. The simulation is compared against experimental results. Future work will consider mapped multiblock grids for practical engineering geometries.

Section: Computational Modeling Of Compressible Navier–stokes Equationsmentioning

confidence: 79%

\overset{normalF}{true}

, is constant, then the second term vanishes, and we only need to derive quadrature formulas for 〈 N T 〉 so that the discrete divergence of a constant vector field is zero.…”

Section: Computational Modeling Of Compressible Navier–stokes Equationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A parallel adaptive numerical method with generalized curvilinear coordinate transformation for compressible Navier–Stokes equations

Owen

Guzik

2016

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

Christopher

Guzik

2022

Self Cite

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.

Adaptive clipping‐and‐redistribution algorithms for bounded and conservative high‐order interpolations applied to discontinuous and reactive flows

Overton‐Katz

Johansen

et al. 2022

Self Cite

A new adaptive clipping-and-redistribution method is presented which provides bounds-preservation for multi-dimensional interpolation in the context of high-order finite-volume discretizations with adaptive mesh refinement (AMR). The underlying finite-volume method (FVM) for the computational fluid dynamics applications is fourth-order accurate for smooth solutions and utilizes AMR for computational efficiency in solving multiscale problems involving turbulence and combustion.High-order interpolation between different AMR levels is required. However, this operation often leads to numerical issues because combustion species must have physical bounds preserved. The present study overcomes two major challenges in the development of the high-order interpolation method. First, the method needs to be bound-preserving near extrema or discontinuities to prevent the emergence of unphysical oscillations while maintaining fourth-order accuracy in smooth flows.Second, the method needs to satisfy the conservation requirement in multiple dimensions, particularly in the context of curvilinear coordinate transformations.Additionally, the method is designed to be localized and computationally inexpensive. The new interpolation scheme is demonstrated by solving reacting flows, which are extremely sensitive to unphysical overshoots in conserved quantities. The test problems are shock-induced H 2 -O 2 combustion and a C 3 H 8 -air flame in a practical bluff-body combustor. Results show the method prevents new extrema near discontinuities while maintaining high-order accuracy in smooth regions. In particular, the method is extremely beneficial for combustion with stiff chemistry. With the proposed new method, even if flame fronts cross AMR interfaces or new grids are created in the vicinity of the flame, solution stability is retained.