A novel numerical flux for the 3D Euler equations with general equation of state

Toro, Eleuterio F.; Castro, Cristóbal E.; Lee, Bok Jik

doi:10.1016/j.jcp.2015.09.037

Cited by 32 publications

(24 citation statements)

References 40 publications

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“…For example, an algorithm similar to that described in [19], which requires isentrope integration, can lead to significant computational costs, on the one hand, and to the loss of the method stability in depression regions, on the other hand. To overcome these difficulties, in [31] the sound speed in the equation of state was obtained by digitally differentiating the tabular pressure values, which provided the same stability and reliability in calculations. A modification of Rowe's linearization method for real gases and its application to a particular case of the Van der Waals gas are presented in [10] and presume introducing an intermediate state as an unknown value of the linearization problem.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Processes in Safety Systems for Substances with Parameters Close to a Critical State

Koroleva¹,

Mishchenkova²,

Tenenev³

et al. 2021

Nelin. Dinam.

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The paper presents a modification of the digital method by S. K. Godunov for calculating real gas flows under conditions close to a critical state. The method is generalized to the case of the Van der Waals equation of state using the local approximation algorithm. Test calculations of flows in a shock tube have shown the validity of this approach for the mathematical description of gas-dynamic processes in real gases with shock waves and contact discontinuity both in areas with classical and nonclassical behavior patterns. The modified digital scheme by Godunov with local approximation of the Van der Waals equation by a two-term equation of state was used for simulating a spatial flow of real gas based on Navier – Stokes equations in the area of a complex shape, which is characteristic of the internal space of a safety valve. We have demonstrated that, under near-critical conditions, areas of nonclassical gas behavior may appear, which affects the nature of flows. We have studied nonlinear processes in a safety valve arising from the movement of the shut-off element, which are also determined by the device design features and the gas flow conditions.

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Section: Introductionmentioning

confidence: 99%

Nonlinear Processes in Safety Systems for Substances with Parameters Close to a Critical State

Koroleva¹,

Mishchenkova²,

Tenenev³

et al. 2021

Nelin. Dinam.

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show abstract

“…Some recent work has aimed to devise efficient, high fidelity general EoS Riemann solvers [5,6] with the EoS in assumed analytic form. Nonetheless, it is vital to test the accuracy of such general EoS Riemann solvers.…”

Section: Introductionmentioning

confidence: 99%

Solving the Riemann problem for realistic astrophysical fluids

Chen

Coleman

Blackman

et al. 2019

Journal of Computational Physics

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We present new methods to solve the Riemann problem both exactly and approximately for general equations of state (EoS) to facilitate realistic modeling and understanding of astrophysical flows. The existence and uniqueness of the new exact general EoS Riemann solution can be guaranteed if the EoS is monotone regardless of the physical validity of the EoS. We confirm that: (1) the solution of the new exact general EoS Riemann solver and the solution of the original exact Riemann solver match when calculating perfect gas Euler equations; (2) the solution of the new Harten-Lax-van Leer-Contact (HLLC) general EoS Riemann solver and the solution of the original HLLC Riemann solver match when working with perfect gas EoS; and (3) the solution of the new HLLC general EoS Riemann solverapproaches the new exact solution. We solve the EoS with two methods, one is to interpolate 2D EoS tables by the bi-linear interpolation method, and the other is to analytically calculate thermodynamic variables at run-time. The interpolation method is more general as it can work with other monotone and realistic EoS, while the analytic EoS solver introduced here works with a relatively idealized EoS. Numerical results confirm that the accuracy of the two EoS solvers is similar. We study the efficiency of these two methods with the HLLC general EoS Riemann solver and find that analytic EoS solver is faster in the test problems. However, we point out that a combination of the two EoS solvers may become favorable in some specific problems. Throughout this research, we assume local thermal equilibrium.

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“…The HLL method is efficient 4 D. SUN ET AL. Further developments for these methods can be found in Refs [10,[13][14][15]. Unfortunately, it cannot resolve contact discontinuity exactly [7].…”

Section: Introductionmentioning

confidence: 99%

“…The differences between those manners are in the energy equation of the convective term: total enthalpy in Liou-Steffen, total energy in Zha-Bigen, and kinetic energy in Toro-Vazquez's splitting. Further developments for these methods can be found in Refs [10,[13][14][15]. Among these splitting manners, Toro-Vazquez splitting seems to be most reasonable, because the advection term contains no pressure terms and all the pressure terms are included in the pressure flux.…”

Section: Introductionmentioning

confidence: 99%

A robust flux splitting method with low dissipation for all‐speed flows

Sun

Yan

et al. 2016

Numerical Methods in Fluids

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Summary In this paper, we propose a simple robust flux splitting method for all‐speed flows with low dissipation. Following the Toro‐Vazquez splitting, the inviscid flux is split into the convective and the pressure parts first. Then, we apply the Harten‐Lax‐van Leer (HLL) algorithm to each parts with low dissipation modification. Here, the modification improves the method with accurately resolving contact discontinuity and high resolution for low speed flows. Several carefully chosen numerical tests are investigated, and the results show that the proposed scheme is capable of resolving contact discontinuity, robust against the shock anomaly and accurate at all‐speeds. Because of these properties, it is expected to be widely applied to all‐speed flow studies. Copyright © 2016 John Wiley & Sons, Ltd.

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A novel numerical flux for the 3D Euler equations with general equation of state

Cited by 32 publications

References 40 publications

Nonlinear Processes in Safety Systems for Substances with Parameters Close to a Critical State

Nonlinear Processes in Safety Systems for Substances with Parameters Close to a Critical State

Solving the Riemann problem for realistic astrophysical fluids

A robust flux splitting method with low dissipation for all‐speed flows

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