An adaptive numerical scheme for high-speed reactive flow on overlapping grids

Henshaw, William D.; Schwendeman, Donald W.

doi:10.1016/s0021-9991(03)00323-1

Cited by 81 publications

(138 citation statements)

References 24 publications

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“…Note here that this slice is sufficiently removed from the computational boundaries so that no disturbance generated at the boundaries has yet had opportunity to interact with it. The computational method is a second-order highresolution Godunov method as discussed in [14]. Errors are computed using the L 1 norm for all primitive quantities and results presented in Table 6 Convergence results for shock polar along the line x = −0.25 for y ∈ [0, 0.2].…”

Section: More Complex Flowsmentioning

confidence: 99%

“…On the other hand, the importance of accurate treatment of all discontinuities, including linear jumps, is paramount in the overall efficacy of a given simulation. The difficulties associated with the computation of discontinuous solutions has been the driver behind such developments as high-resolution methods [10][11][12] and adaptive mesh refinement [13,14].…”

Section: Introductionmentioning

confidence: 99%

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On sub-linear convergence for linearly degenerate waves in capturing schemes

Banks

Aslam

Rider

2008

Journal of Computational Physics

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A common attribute of capturing schemes used to find approximate solutions to the Euler equations is a sub-linear rate of convergence with respect to mesh resolution. Purely nonlinear jumps, such as shock waves produce a first-order convergence rate, but linearly degenerate discontinuous waves, where present, produce sub-linear convergence rates which eventually dominate the global rate of convergence. The classical explanation for this phenomenon investigates the behavior of the exact solution to the numerical method in combination with the finite error terms, often referred to as the modified equation. For a first-order method, the modified equation produces the hyperbolic evolution equation with second-order diffusive terms. In the frame of reference of the traveling wave, the solution of a discontinuous wave consists of a diffusive layer that grows with a rate of t 1/2 , yielding a convergence rate of 1/2. Self-similar heuristics for higher order discretizations produce a growth rate for the layer thickness of ∆t 1/(p+1) which yields an estimate for the convergence rate as p/(p+1) where p is the order of the discretization. In this paper we show that this estimated convergence rate can be derived with greater rigor for both dissipative and dispersive forms of the discrete error. In particular, the form of the analytical solution for linear modified equations can be solved exactly. These estimates and forms for the error are confirmed in a variety of demonstrations ranging from simple linear waves to multidimensional solutions of the Euler equations.

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Section: More Complex Flowsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On sub-linear convergence for linearly degenerate waves in capturing schemes

Banks

Aslam

Rider

2008

Journal of Computational Physics

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“…The second special case involves a more difficult set of equations given by the reactive Euler equations. This set of equations was considered in our previous papers [2] and [3] for two-dimensional flow in stationary and moving domains. Here, our focus is on reactive and non-reactive flow in three dimensions for which we consider the nonlinear conservation equations given by…”

Section: Model Equationsmentioning

confidence: 99%

“…The first is a linear advection-diffusion equation, and the second is the (nonlinear) reactive Euler equations of gas dynamics. The first equation provides a useful test case to study the behavior of the numerical approach and to verify its accuracy quantitatively, while the second builds on our earlier work in [2,3] and illustrates the numerical approach for a more difficult set of equations. While a brief description of the discretization of these two PDEs is given, the emphasis of the discussion is on the extension of the numerical approach for parallel computations in three-dimensional geometries.…”

Section: Introductionmentioning

confidence: 99%

“…Other pioneering work includes that of Starius [6][7][8], Kreiss [9], and Steger et al [10] who referred to the approach as Chimera grids. Since this early work, the overlapping grid technique has been used successfully to solve a wide variety of problems in high-speed reactive flow [2,3,11], reactive and non-reactive multi-material flow [12,13], combustion [14], aerodynamics [15][16][17][18][19][20][21], blood flow [22], flows around ships [23], visco-elastic flows [24], and flows with deforming boundaries [25][26][27], among others. The use of AMR in combination with overlapping grids was considered by Brislawn et al [28], Boden and Toro [29], Meakin [21], Henshaw and Schwendeman [2,3], and Banks et al [12,13].…”

Section: Introductionmentioning

confidence: 99%

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Parallel computation of three-dimensional flows using overlapping grids with adaptive mesh refinement

Henshaw¹,

Schwendeman²

2008

Journal of Computational Physics

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This paper describes an approach for the numerical solution of time-dependent partial differential equations in complex three-dimensional domains. The domains are represented by overlapping structured grids, and block-structured adaptive mesh refinement (AMR) is employed to locally increase the grid resolution. In addition, the numerical method is implemented on parallel distributed-memory computers using a domain-decomposition approach. The implementation is flexible so that each base grid within the overlapping grid structure and its associated refinement grids can be independently partitioned over a chosen set of processors. A modified bin-packing algorithm is used to specify the partition for each grid so that the computational work is evenly distributed amongst the processors. All components of the AMR algorithm such as error estimation, regridding, and interpolation are performed in parallel.The parallel time-stepping algorithm is illustrated for initial-boundary-value problems involving a linear advectiondiffusion equation and the (nonlinear) reactive Euler equations. Numerical results are presented for both equations to demonstrate the accuracy and correctness of the parallel approach. Exact solutions of the advection-diffusion equation are constructed, and these are used to check the corresponding numerical solutions for a variety of tests involving different overlapping grids, different numbers of refinement levels and refinement ratios, and different numbers of processors. The problem of planar shock diffraction by a sphere is considered as an illustration of the numerical approach for the Euler equations, and a problem involving the initiation of a detonation from a hot spot in a T-shaped pipe is considered to demonstrate the numerical approach for the reactive case. For both problems, the solutions are shown to be well resolved on the finest grid. The parallel performance of the approach is examined in detail for the shock diffraction problem.

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Direct numerical simulations of dynamic gas‐solid suspensions

2016

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We report direct numerical simulation results for gas flow through dynamic suspensions of spherical particles. The simulations are performed using an immersed boundary method (IBM), with careful correction for the grid resolution effect. The flow systems we have studied vary with mean flow Reynolds number, solids volume fraction, as well as particle/gas density ratio. On the basis of the simulation results, the effect of particle mobility on the gas-solid drag force is analyzed and introduced into the existing drag correlation that was derived from simulations of stationary particles. This mobility effect is characterized by the granular temperature, which is a result of the particle velocity fluctuation. The modified drag correlation is considered so-far the most accurate expression for the interphase momentum exchange in computational fluid dynamics models, in which the gas-solid interactions are not directly resolved.

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An adaptive numerical scheme for high-speed reactive flow on overlapping grids

Cited by 81 publications

References 24 publications

On sub-linear convergence for linearly degenerate waves in capturing schemes

On sub-linear convergence for linearly degenerate waves in capturing schemes

Parallel computation of three-dimensional flows using overlapping grids with adaptive mesh refinement

Direct numerical simulations of dynamic gas‐solid suspensions

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