Computation of reactive duct flows in external fields

Ben‐Artzi, Matania; Birman, A.

doi:10.1016/0021-9991(90)90099-m

Cited by 13 publications

(10 citation statements)

References 11 publications

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“…As explained in [6], this error is due to the ''startup" of the captured shock near the center, where the numerical dissipation generates an entropy higher than the exact value. These discrepancies can be weakened by using the exact value of solution as the boundary data at the center [3], which is actually impractical. We can see that our scheme produces a good result in Fig.…”

Section: Noh Problemmentioning

confidence: 97%

“…The discretization of source term is realized with the mid-point rule in time and the trapezoidal rule in space in order to balance the variation of fluxes well, which is an important factor to devise a well-balanced scheme, see Remark 2.3. The purpose of this work is to extend the GRP scheme to solve the radially symmetric flows and the resulting scheme is different from [3,12,22]. We pay our special attention to the treatment of the geometrical singularity at the center and the numerical boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

“…In [3,12] the GRP method was used to track discontinuities. Their focus was not on the numerical treatment of the singularity at the center, but on the geometrical effect on numerical fluxes.…”

Section: Introductionmentioning

confidence: 99%

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Implementation of the GRP scheme for computing radially symmetric compressible fluid flows

Liu

Sun

2009

Journal of Computational Physics

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Section: Noh Problemmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

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Implementation of the GRP scheme for computing radially symmetric compressible fluid flows

Liu

Sun

2009

Journal of Computational Physics

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“…On the one hand, there is the generalized Riemann problem (GRP) (van Leer 1979 ; Ben-Artzi 1989 ; LeFloch and Raviart 1988 ; Bourgeade et al. 1989 ; Ben-Artzi and Birman 1990 ; Ben-Artzi and Falcovitz 1984 , 2003 ; LeFloch and Raviart 1988 ; Qian et al. 2014 ; Goetz and Iske 2016 and Goetz and Dumbser 2016 ; Goetz et al.…”

Section: Introductionmentioning

confidence: 99%

Higher-order accurate space-time schemes for computational astrophysics—Part I: finite volume methods

Balsara

2017

Living Rev Comput Astrophys

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As computational astrophysics comes under pressure to become a precision science, there is an increasing need to move to high accuracy schemes for computational astrophysics. The algorithmic needs of computational astrophysics are indeed very special. The methods need to be robust and preserve the positivity of density and pressure. Relativistic flows should remain sub-luminal. These requirements place additional pressures on a computational astrophysics code, which are usually not felt by a traditional fluid dynamics code. Hence the need for a specialized review. The focus here is on weighted essentially non-oscillatory (WENO) schemes, discontinuous Galerkin (DG) schemes and PNPM schemes. WENO schemes are higher order extensions of traditional second order finite volume schemes. At third order, they are most similar to piecewise parabolic method schemes, which are also included. DG schemes evolve all the moments of the solution, with the result that they are more accurate than WENO schemes. PNPM schemes occupy a compromise position between WENO and DG schemes. They evolve an Nth order spatial polynomial, while reconstructing higher order terms up to Mth order. As a result, the timestep can be larger. Time-dependent astrophysical codes need to be accurate in space and time with the result that the spatial and temporal accuracies must be matched. This is realized with the help of strong stability preserving Runge-Kutta schemes and ADER (Arbitrary DERivative in space and time) schemes, both of which are also described. The emphasis of this review is on computer-implementable ideas, not necessarily on the underlying theory.

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“…Widely used augmented Euler formulations include additional evolution equations describing the mass fraction or volume fraction of a material, or the ratio of specific heats 𝛾 for the mixture. The corresponding models are the mass fraction model [6,33,47] (including the reactive flows with mass fractions of burnt/unburnt materials [9,7]), the volume fraction model [52] and the 𝛾-model [1,30,52]. In the mixing region with more than one material across material interfaces, an equation of state for the mixture is required for such a task.…”

Section: Introductionmentioning

confidence: 99%

An energy-splitting high order numerical method for multi-material flows

Lei¹,

Li²

2020

Preprint

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This chapter deals with multi-material flow problems by a kind of effective numerical methods, based on a series of reduced forms of the Baer-Nunziato (BN) model. Numerical simulations often face a host of difficult challenges, typically including the volume fraction positivity and stability of multi-material shocks. To cope with these challenges, we propose a new non-oscillatory energy-splitting Godunovtype scheme for computing multi-fluid flows in the Eulerian framework. A novel reduced version of the BN model is introduced as the basis for the energy-splitting scheme. In comparison with existing two-material compressible flow models obtained by reducing the BN model in the literature, it is shown that our new reduced model can simulate the kinetic energy exchange around material interfaces very effectively. Then a second-order accurate extension of the energy-splitting Godunov-type scheme is made using the generalized Riemann problem (GRP) solver. Numerical experiments are carried out for the shock-interface interaction, shock-bubble interaction and the Richtmyer-Meshkov instability problems, which demonstrate the excellent performance of this type of schemes.

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Computation of reactive duct flows in external fields

Cited by 13 publications

References 11 publications

Implementation of the GRP scheme for computing radially symmetric compressible fluid flows

Implementation of the GRP scheme for computing radially symmetric compressible fluid flows

Higher-order accurate space-time schemes for computational astrophysics—Part I: finite volume methods

An energy-splitting high order numerical method for multi-material flows

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