High-order finite-volume methods for hyperbolic conservation laws on mapped multiblock grids

McCorquodale, Peter; Dorr, M.; Hittinger, Jeffrey; Colella, Phillip

doi:10.1016/j.jcp.2015.01.006

Cited by 26 publications

(26 citation statements)

References 38 publications

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“…The method is motivated by that in [32] for Cartesian grids, extended to mapped grids in [10] and to mapped multiblock grids in [31]. What is new here is that we are calculating on a 2D manifold in 3D and also that we have vector components that require a basis transformation (Step (2) below).…”

Section: Spatial Discretizationmentioning

confidence: 99%

“…Step (2). The procedure for finding the stencil is explained in [31]. The set of grid cells in the stencil is found as follows.…”

Section: Spatial Discretizationmentioning

confidence: 99%

“…(2) Interpolate U from to the ghost cells Ᏻ 3,3 ( ) − by the method of least squares from stencils in [31]. See Figure 2 for an illustration of interpolation stencils for two sample ghost cells.…”

Section: Spatial Discretizationmentioning

confidence: 99%

“…For the scalar component h of U , we follow the procedure in [31], approximating h by a Taylor polynomial over latitude and longitude and finding its coefficients a pq for p, q ≥ 0 and p + q ≤ 3 satisfying as closely as possible the overdetermined system of N equations p,q≥0; p+q≤3…”

Section: Spatial Discretizationmentioning

confidence: 99%

“…We apply these methods on cubed-sphere meshes, which consist of six panels with a separate mapping on each panel. To coordinate the different mappings along panel boundaries, we use the mapped-multiblock approach of [31] with the following modifications:…”

Section: Introductionmentioning

confidence: 99%

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An adaptive multiblock high-order finite-volume method for solving the shallow-water equations on the sphere

McCorquodale

Ullrich

Johansen

et al. 2015

Commun. Appl. Math. Comput. Sci.

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We present a high-order finite-volume approach for solving the shallow-water equations on the sphere, using multiblock grids on the cubed sphere. This approach combines a Runge-Kutta time discretization with a fourth-order-accurate spatial discretization and includes adaptive mesh refinement and refinement in time. Results of tests show fourth-order convergence for the shallow-water equations as well as for advection in a highly deformational flow. Hierarchical adaptive mesh refinement allows solution error to be achieved that is comparable to that obtained with uniform resolution of the most refined level of the hierarchy but with many fewer operations.

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Section: Spatial Discretizationmentioning

confidence: 99%

“…Step (2). The procedure for finding the stencil is explained in [31]. The set of grid cells in the stencil is found as follows.…”

Section: Spatial Discretizationmentioning

confidence: 99%

Section: Spatial Discretizationmentioning

confidence: 99%

Section: Spatial Discretizationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

An adaptive multiblock high-order finite-volume method for solving the shallow-water equations on the sphere

McCorquodale

Ullrich

Johansen

et al. 2015

Commun. Appl. Math. Comput. Sci.

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Continuum kinetic modelling of cross‐separatrix plasma transport in a tokamak edge including self‐consistent electric fields

Dorf

Dorr

2018

Contributions to Plasma Physics

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Eulerian kinetic calculations are presented for the axisymmetric cross‐separatrix plasma transport at the edge of a tokamak. The simulations are performed with a high‐order finite volume code COGENT, which solves the long‐wavelength limit of the full‐f ion gyrokinetic equation including the non‐linear Fokker–Plank collision model. Self‐consistent 2D electrostatic potential variations are obtained from the quasi‐neutrality (∇·j = 0) equation coupled to an isothermal fluid electron response. Illustrative solutions presented for parameters characteristic of the DIII‐D tokamak show qualitative agreement with experimental data.

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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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High-order finite-volume methods for hyperbolic conservation laws on mapped multiblock grids

Cited by 26 publications

References 38 publications

An adaptive multiblock high-order finite-volume method for solving the shallow-water equations on the sphere

An adaptive multiblock high-order finite-volume method for solving the shallow-water equations on the sphere

Continuum kinetic modelling of cross‐separatrix plasma transport in a tokamak edge including self‐consistent electric fields

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

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