An immersed boundary method for simulation of inviscid compressible flows

Zhang, Y.; Zhou, Chunhua

doi:10.1002/fld.3872

Cited by 16 publications

(17 citation statements)

References 31 publications

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“…To save the computational cost, the adaptive mesh is applied to refine the regions containing the wing and the high-gradient field. 27,30 The computed profiles of surface pressure coefficient C P at 6 spanwise sections (x = 0.2, 0.44, 0.65, 0.8, 0.9, 0.95) are presented and compared with the experimental data 31 and the numerical results obtained by Navier-Stokes solver, 30 see Figure 19A-F. We can see that for the C P on the upper surface, all the solutions seem to be overpredicted. Figure 18 shows the pressure contour lines on the upper and lower surface of the wing.…”

Section: Transonic Flow Over Onera M6 Wingmentioning

confidence: 95%

“…26,27,29 However, it has been pointed out that it is difficult to obtain a precise solution even though the overall flow pattern can be predicted with a low grid resolution. The selected test cases have been studied widely by many researchers.…”

Section: Flow Over Naca0012 Airfoilmentioning

confidence: 99%

“…27,30 We use the level-set method to represent the 3-D wing implicitly by defining the signed distance function from a STL file of an ONERA M6 wing model. The ONERA M6 wing has been studied by many researchers to validate the compressible flow solvers using inviscid Euler equations or the Navier-Stokes equations.…”

Section: Transonic Flow Over Onera M6 Wingmentioning

confidence: 99%

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An immersed boundary solver for inviscid compressible flows

Liu

2017

Numerical Methods in Fluids

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Summary In this paper, a simple and efficient immersed boundary (IB) method is developed for the numerical simulation of inviscid compressible Euler equations. We propose a method based on coordinate transformation to calculate the unknowns of ghost points. In the present study, the body‐grid intercept points are used to build a complete bilinear (2‐D)/trilinear (3‐D) interpolation. A third‐order weighted essentially nonoscillation scheme with a new reference smoothness indicator is proposed to improve the accuracy at the extrema and discontinuity region. The dynamic blocked structured adaptive mesh is used to enhance the computational efficiency. The parallel computation with loading balance is applied to save the computational cost for 3‐D problems. Numerical tests show that the present method has second‐order overall spatial accuracy. The double Mach reflection test indicates that the present IB method gives almost identical solution as that of the boundary‐fitted method. The accuracy of the solver is further validated by subsonic and transonic flow past NACA2012 airfoil. Finally, the present IB method with adaptive mesh is validated by simulation of transonic flow past 3‐D ONERA M6 Wing. Global agreement with experimental and other numerical results are obtained.

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Section: Transonic Flow Over Onera M6 Wingmentioning

confidence: 95%

Section: Flow Over Naca0012 Airfoilmentioning

confidence: 99%

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An immersed boundary solver for inviscid compressible flows

Liu

2017

Numerical Methods in Fluids

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“…Although the principle of discrete forcing in the present study is similar to the one in the aforementioned work, 27 we borrow aspects of interpolation strategies in the work of Mo et al 23 for the proposed IB method. It can be seen that most studies have employed the ghost-cell IB methodology, and the only effort using the HCIB approach is limited to low-speed compressible flows.…”

Section: Introductionmentioning

confidence: 99%

A sharp‐interface immersed boundary framework for simulations of high‐speed inviscid compressible flows

Brahmachary

Natarajan

Kulkarni

et al. 2017

Numerical Methods in Fluids

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Summary A new finite‐volume flow solver based on the hybrid Cartesian immersed boundary (IB) framework is developed for the solution of high‐speed inviscid compressible flows. The IB method adopts a sharp‐interface approach, wherein the boundary conditions are enforced on the body geometry itself. A key component of the present solver is a novel reconstruction approach, in conjunction with inverse distance weighting, to compute the solutions in the vicinity of the solid‐fluid interface. We show that proposed reconstruction leads to second‐order spatial accuracy while also ensuring that the discrete conservation errors diminish linearly with grid refinement. Investigations of supersonic and hypersonic inviscid flows over different geometries are carried out for an extensive validation of the proposed flow solver. Studies on cylinder lift‐off and shape optimisation in supersonic flows further demonstrate the efficacy of the flow solver for computations with moving and shape‐changing geometries. These studies conclusively highlight the capability of the proposed IB methodology as a promising alternative for robust and accurate computations of compressible fluid flows on nonconformal Cartesian meshes.

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“…NEP has been successfully implemented in gas dynamics and other conservation laws by a number of authors, such as Ersoy et al [2], Golay [3] and Puppo [12,13]. NEP can also be used to investigate the accuracy of numerical methods [14]. Alternative types of smoothness indicators were discussed in [8,9].…”

Section: Introductionmentioning

confidence: 99%

Numerical Entropy Production of the One-and-a-Half-Dimensional Shallow Water Equations With Topography

Mungkasi

2015

JIMS

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Abstract. Numerical entropy production can be used as a smoothness indicator of solutions to conservation laws. By definition the entropy production is non-positive. However some authors, using a finite volume method framework, showed that positive overshoots of the numerical entropy production were possible for conservation laws (no source terms involved). Note that the one-and-a-half-dimensional shallow water equations without source terms are conservation laws. A report has been published regarding the behaviour of the numerical entropy production of the oneand-a-half-dimensional shallow water equations without source terms. The main result of that report was that positive overshoots of the numerical entropy production were avoided by use of a modified entropy flux which satisfies a discrete numerical entropy inequality. In the present article we consider an extension problem of the previous report. We take the one-and-a-half-dimensional shallow water equations involving topography. The topography is a source term in the considered system of equations. Our results confirm that a modified entropy flux which satisfies a discrete numerical entropy inequality is indeed required to have no positive overshoots of the entropy production.Key words and Phrases: Numerical entropy production, shallow water equations, smoothness indicator, finite volume method. S. MungkasiAbstrak. Produksi entropi numeris dapat digunakan sebagai indikator kehalusan fungsi penyelesaian hukum-hukum kekekalan. Berdasarkan definisi, produksi entropi adalah tak-positif. Namun demikian, menggunakan suatu kerangka metode volume hingga beberapa peneliti menunjukkan bahwa produksi entropi numeris bisa saja bernilai positif pada titik-titik tertentu untuk hukum-hukum kekekalan (tidak ada suku sumber dalam persamaan yang diselesaikan). Perlu dicatat bahwa persamaan air dangkal satu setengah dimensi yang tidak melibatkan suku sumber merupakan hukum kekekalan. Sebuah laporan tentang perilaku produksi entropi numeris untuk persamaan air dangkal satu setengah dimensi tanpa suku sumber telah diterbitkan. Hasil utama laporan tersebut adalah nilai positif produksi entropi numeris dapat dihindari menggunakan flux entropi termodifikasi yang memenuhi suatu pertidaksamaan entropi numeris diskret. Dalam artikel saat ini, dipandang suatu masalah yang lebih umum, yaitu persamaan air dangkal satu setengah dimensi yang melibatkan topografi. Topografi ini adalah suatu suku sumber dalam sistem persamaan yang dipandang. Hasil dalam artikel ini menegaskan bahwa suatu flux entropi termodifikasi yang memenuhi suatu pertidaksamaan entropi numeris diskret memang sungguh-sungguh diperlukan untuk menghindari timbulnya produksi entropi yang bernilai positif.Kata kunci: Produksi entropi numeris, persamaan air dangkal, indikator kehalusan, metode volume hingga.

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An immersed boundary method for simulation of inviscid compressible flows

Cited by 16 publications

References 31 publications

An immersed boundary solver for inviscid compressible flows

An immersed boundary solver for inviscid compressible flows

A sharp‐interface immersed boundary framework for simulations of high‐speed inviscid compressible flows

Numerical Entropy Production of the One-and-a-Half-Dimensional Shallow Water Equations With Topography

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