An enhanced AUSM
                
                  
                
                $$^{+}$$
                
                  
                    
                      
                      +
                    
                  
                
              -up scheme for high-speed compressible two-phase flows on hybrid grids

Pandare, Aditya; Luo, Hong; Bakosi, József

doi:10.1007/s00193-018-0861-x

Cited by 15 publications

(4 citation statements)

References 46 publications

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“…However, as a consequence interfaces are smeared over multiple computational cells. A large effort has been directed towards sharpening of this interface via algebraic methods [19,20,21,22] in the context of interface capturing multi-fluid models. Most of the work in this direction attempts at bypassing the TVD condition for limiting the volume-fraction and using a compressive limiting function instead.…”

Section: Numerical Methods For Multi-materials Hydrodynamicsmentioning

confidence: 99%

“…This is followed by a description of the method to compute derivatives of velocity and volume-fractions for the volume integrals in Eqs. (18) and (21) in §3.5. The high-order solution has to be limited in a consistent way for the method to be stable and non-oscillatory while solving discontinuous and non-linear problems.…”

Section: Weno(p2) Limitingmentioning

confidence: 99%

“…The AUSM + flux has been successfully used for a single-pressure two-velocity two-phase system for inviscid [17,43,21] and turbulent [46] applications. However, to the best of the authors' knowledge, the AUSM + flux has not been used to solve the pressure non-equilibrium multi-material system.…”

Section: Riemann Solvermentioning

confidence: 99%

“…(1) are calculated as regular volume integral terms, as shown in Eqs. (18) and (21). Gaussian quadrature is used to perform these integral calculations numerically.…”

Section: Pressure Relaxation Source Termsmentioning

confidence: 99%

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A reconstructed discontinuous Galerkin method for multi‐material hydrodynamics with sharp interfaces

Pandare

Waltz

Bakosi

2020

Numerical Methods in Fluids

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Discontinuous Galerkin (DG) methods have been well established for single material hydrodynamics. However, consistent DG discretizations for non-equilibrium multi-material (more than two materials) hydrodynamics have not been extensively studied. In this work, a novel reconstructed discontinuous Galerkin (rDG) method for the single-velocity multi-material system is presented. The multi-material system being considered assumes stiff velocity relaxation, but does not assume pressure and temperature equilibrium between the multiple materials. A second-order DG(P 1 ) method and a third-order least-squares based rDG(P 1 P 2 ) are used to discretize this system in space, and a third-order TVD Runge-Kutta method is used to integrate in time. A well-balanced DG discretization of the non-conservative system is presented, and is verified by numerical test problems. Further, a consistent interface treatment is implemented, which ensures strict conservation of material masses and total energy. Numerical tests indicate that the DG and rDG methods are indeed second-and third-order accurate. Comparisons with the second-order finite volume method show that the DG and rDG methods are able to capture the interfaces more sharply. The DG and rDG methods are also more accurate in the single-material regions of the flow. This work focuses on the general multidimensional rDG formulation of the non-equilibrium multi-material system and a study of properties of the method via one-dimensional numerical experiments. The results from this research will be the foundation for a multi-dimensional high-order rDG method for multi-material hydrodynamics.

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Section: Numerical Methods For Multi-materials Hydrodynamicsmentioning

confidence: 99%

Section: Weno(p2) Limitingmentioning

confidence: 99%

Section: Riemann Solvermentioning

confidence: 99%

“…(1) are calculated as regular volume integral terms, as shown in Eqs. (18) and (21). Gaussian quadrature is used to perform these integral calculations numerically.…”

Section: Pressure Relaxation Source Termsmentioning

confidence: 99%

See 2 more Smart Citations

A reconstructed discontinuous Galerkin method for multi‐material hydrodynamics with sharp interfaces

Pandare

Waltz

Bakosi

2020

Numerical Methods in Fluids

Self Cite

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An improvement of the AUSMDV$$^{+}$$ scheme on unstructured grids

Phongthanapanich

Matthujak

2021

Shock Waves

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It is well known that many contact-and shear-preserving approximate Riemann solvers admit various forms of numerical shock anomalies and numerical shock instabilities such as the carbuncle phenomenon, sonic glitch, and post-shock wave oscillations. Recently, the AUSMDV + scheme was developed to improve the numerical stability and accuracy of the AUSMDV scheme. For the AUSMDV + scheme, the AUSMD + and the AUSMV + schemes were introduced as the accurate and the moderately dissipative schemes, respectively. In this paper, the AUSMDV2 + scheme is presented as an improved version of the AUSMDV + scheme. In the AUSMDV2 + scheme, a newly proposed mass flux function is used for both the AUSMD + and the AUSMV + schemes. Additionally, a new normalized weighting function is proposed to control the amount of dissipation. Many tests show that the proposed scheme's stability and accuracy are easily controlled by varying the constant parameter κ between 0.1 and 1.0. Furthermore, the dissipation mechanism of the scheme is studied by employing linearized discrete analysis on the odd-even decoupling problem. The resulting recursive equations show that the proposed scheme can effectively damp out all perturbations over time. Finally, the scheme's numerical stability and accuracy are examined in several test cases on structured and unstructured grids with the first-and second-order accurate methods. The results show that the proposed scheme is stable, accurate, and suitable for solving a wide range of high-speed compressible flow problems.

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A Review of Riemann Solvers for Hypersonic Flows

Sun

Liu

et al. 2021

Arch Computat Methods Eng

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In the design of the hypersonic airliner which can greatly shorten the flight time and conduct space travel, it is of great significance for a Riemann solver to accurately simulate hypersonic flows. In this survey, the research process on the Riemann solver for hypersonic flows is reviewed, including the constructions of the traditional Riemann solvers, improvements of the traditional Riemann solvers for the shock anomaly, and the importance of the all-speed Riemann solver for hypersonic flows. Moreover, constructions and applications of the all-speed Riemann solvers are presented. It is obvious that the Riemann solver should be capable of obtaining physical solutions at low speeds and be robust against shock anomaly near strong shocks at the same time in simulating hypersonic flows.

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An enhanced AUSM $$^{+}$$ + -up scheme for high-speed compressible two-phase flows on hybrid grids

Cited by 15 publications

References 46 publications

A reconstructed discontinuous Galerkin method for multi‐material hydrodynamics with sharp interfaces

A reconstructed discontinuous Galerkin method for multi‐material hydrodynamics with sharp interfaces

An improvement of the AUSMDV$$^{+}$$ scheme on unstructured grids

A Review of Riemann Solvers for Hypersonic Flows

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