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In computational fluid dynamics of compressible fluid flow, the simple low-dissipation advection upstream (SLAU) scheme formulated with multidimensional velocity components (normal and parallel to a cell interface) is a widely employed all-speed scheme. As a variant of SLAU, the mSLAU scheme, which adopts only a velocity component normal to the cell interface instead of multidimensional velocity components, is used for rotorcraft calculations. However, although mSLAU has been claimed to be empirically stable, it has been pointed out that using only the cell-interface-normal velocity component instead of the multidimensional velocity components causes numerical instability. Therefore, to clarify the roles of the multidimensional velocity components for computational stability, we solved some benchmark problems associated with using SLAU or mSLAU. We discovered that the multidimensional velocity components contributed to stability against poor-quality grids by isotropically producing enough amount of numerical dissipation, especially in low-subsonic and supersonic flows. Although mSLAU could practically treat moderate Mach number flows (approximately 0.1

A slender-bodied vehicle with asymmetrically arranged protuberance generates strong side force due to asymmetric vortices, even at a low angle-of-attack. We investigated effects of the well-known RANS turbulence models [SA-R (Crot = 0.0, 1.0, and 2.0), SST, and SST-2003] by comparing the numerically obtained side force values on supersonic slender-body, along with the flow structure. As a result, all the SA-R models showed good agreement with the experiment regardless of the Crot (which controls the degree of modification from the original SA model), although a separation point on the protuberance side slightly changed depending on the Crot value. On the other hand, as for the SST models, when the vorticity was used to evaluate eddy viscosity (original SST) the side force exhibit 44% deviation from the experiment, whereas SST-2003, in which the strain rate was employed instead, significantly reduced the discrepancy to 0.7%.

There are growing attentions to providing a simple and accurate shock detection method for computational fluid dynamics, not only for identifying the shocks in the post-processing but also for developing low-dissipation numerical schemes. However, most of conventional methods are designed for only either of them, as represented by Kanamori-Suzuki sensor [22] and Ducros sensor [1999]. The former method is quite accurate in inviscid flows but rather expensive to be incorporated into a numerical scheme, whereas the latter is very efficient and widely used while calling for an expert's care in determining actual shocks. In order to achieve both efficiency and theoretical accuracy, we developed a novel shock detection method for two-dimensional viscous/inviscid flows on Cartesian grids based on Canny-Edge-Detection [29] , which is a well-known image processing method. We successfully applied the Canny-Edge-Detection to computational fluid dynamics (CFD) solutions by replacing the brightness value of digital images with pressure in CFD solutions. Then, by taking advantages of the simplicity of Canny-Edge-Detection along with Rankine-Hugoniot conditions across shocks (where 50% deviation is intentionally allowed only within the numerically captured shock), our method is designed to be both efficient and theoretically accurate, in contrast with the conventional schemes. The detection results of our method are examined in selected three test cases, in comparison with the Kanamori-Suzuki sensor and the Ducros sensor. Through the tests, we confirmed that our sensor is as accurate as Kanamori-Suzuki method, while as cheap as the Ducros sensor. In addition, the present sensor successfully detects shocks even in a viscous flow, and smoothly represents shocks oblique to the grid lines. Therefore, our sensor is eventually expected to contribute not only to the post-processing in CFD but also to developing schemes for computing high-speed flows with low cost and high accuracy.

SLAU2 and AUSMPW + , both categorized as AUSM-type Riemann solvers, have been extensively developed in gasdynamics. They are based on a splitting of the numerical flux into advected and pressure parts. In this paper, these two Riemann solvers have been extended to magnetohydrodynamics (MHD). The SLAU2 Riemann solver has the favorable attribute that its dissipation for low-speed flows scales as O(M2) , where M is the Mach number. This is the physical scaling required for low-speed flows, and the dissipation in SLAU2 for MHD is engineered to have this low Mach number scaling. The AUSMPW + , when its pressure flux is replaced with that of SLAU2, has the same low Mach number scaling. At higher Mach numbers, however, the pressure-split Riemann solvers were found not to function well for some MHD Riemann problems, despite the fact that they were engineered to have a dissipation that scales as O(|M|) for high Mach number flows. The HLLI Riemann solver (Dumbser and Balsara in J Comput Phys 304:275–319, 2016) has a dissipation that scales as O(|M|) , which makes it unsuitable for low Mach number flows. However, it has very favorable performance for higher Mach number MHD flows. Since the two families of Riemann solvers perform very well over a range of intermediate Mach numbers, the best way to benefit from the mutually complementary strengths of both these Riemann solvers is to hybridize between them. The result is an all-speed Riemann solver for MHD. We, therefore, document hybridized SLAU2–HLLI and AUSMPW + –HLLI Riemann solvers. The hybrid Riemann solvers suppress the oscillations that appeared in single-solver solutions, and they also preserve contact discontinuities, as well as Alfvén waves, very well. Furthermore, their better resolution at low speeds has been demonstrated. We also present several stringent one-dimensional test problems., This is a post-peer-review, pre-copyedit version of an article published in "Shock Waves". The final authenticated version is available online at: http://dx.doi.org/10.1007/s00193-018-0842-0

Accepted: 2018-02-18, 資料番号: SA1180403000

Most of flight vehicles have various protuberant devices on their surfaces, but asymmetry in their positioning with respect to the body axis can affect aerodynamic characteristics of vehicles, particularly roll moment. Thus, it is important in rocket development to clarify the effects of the protuberances on the vehicle aerodynamic characteristics. In this study, as a basic research, we systematically investigated such effects using CFD, by changing the positions of a protuberance. As a result, the roll moment increased nearly linearly with angle of attack (=α), but its trend was different in protuberance locations, particularly when arranged near the center-of-gravity. In positioning there at α = 20 °, the wake vortex center moved farther away from protuberance compared with α = 15 °, then the pressure decline at its wake side was suppressed, and thus, the pressure difference between its upstream and downstream sides became smaller. As a consequence, the roll moment did not arise linearly, but decreased at α = 20 °.

A supersonic parachute is one of effective and promising deceleration processes at entry into a planet. However, fundamental researches on its aerodynamics, particularly at its opening phase, have not been fully carried out. In this study, flow fields in/around simple configurations that modeled a supersonic parachute at its opening are discussed using computed fluid dynamics. Results indicate that pressure inside the parachute is exposed to twice (at the maximum) as large as the pitot pressure at Mach 2. In addition, the so-called “breathing,” which is a more characteristic unsteady phenomenon, appears due to the internal pressure fluctuation, which changes the position of the detached shock wave periodically. Finally, at a higher Reynolds number, the boundary-layer inside the parachute became thinner, leading to more complex shock/boundary-layer interactions.

The development of a fully reusable vertical-takeoff-and-vertical-landing (VTVL) rocket is indispensable for reducing space transportation costs. However, there are many technical issues associated with such vehicles, such as turnover maneuvers during return flight where the pitching moment plays a key role. It is known that aerodynamic characteristics can be controlled by installing aerodynamic devices, but the relationship between the aerodynamic characteristics and the flowfields has not been explored. To clarify this relationship using computational fluid dynamics (CFD), we investigated these flowfields and aerodynamic characteristics, in the case where we install such devices (fins) in the nose part of a reusable rocket. We found that vortices form downstream of the aerodynamic devices. For angles of attack between 0 and 90 degrees (in which the fins are located in the upstream portion), these vortices significantly affect the surface pressure on the rocket and increase the pitching moment. On the other hand, for AOAs between 90 to 180 degrees (in which the fins are in the downstream portion), the effect of these vortices on the on-surface pressure is negligible, and only vortices formed near the surface of the fins increase the pitching moment.

In the aerodynamic characteristics of supersonic parachutes, it is important to understand surface pressure distribution because it is strongly related to the fluctuation of drag and problematic unstable deformation of a parachute. However, there is a paucity of studies that focuses on the detailed surface pressure distribution. Therefore, we investigated the interior and exterior of a rigid disk-gap-band-type parachute as the first step, under the assumption that the forebody or suspension lines are absent, and thus the pressure and drag fluctuations are small. Two configurations are considered: one with a continuous gap and a vent orifice, representing a conventional Disk-Gap-Band parachute, and one with a discontinuous gap made up of 8 separate orifices and a vent orifice. By making the gap discontinuous, the interior and exterior pressure fluctuations are reduced. Furthermore, as indicated by the flowfield analysis, the discrete gap reduces the asymmetric pressure distribution interior the parachute, and the interior pressure fluctuation far from the center is suppressed. The result is considered useful for the suppression of unstable deformation such as area oscillation. This is currently a problem in supersonic parachute operation. In addition, we have identified locations on the model surface where the pressure fluctuations contribute to the drag fluctuations of the model.

SLAU2 (Simple Low-dissipation Advection-Upstream-splitting-method 2) numerical flux function, one of AUSM-type methods (3-wave solver), originally developed and widely used in gasdynamics, has been applied to two-dimensional magnetohydrodynamics (MHD) simulations. According to numerical tests for a wide range of flow and magnetic conditions, its reliability, efficiency, and accuracy have been demonstrated: i) Robustness of SLAU2 against shock-anomalies (e.g., carbuncle phenomena) has been confirmed in the MHD-extended version of our hypersonic flow test; ii) The computational cost has been reduced for approximately 3% compared with HLLD (Harten-Lax-van_Leer with Discontinuities), a more expensive, 5-wave solver; iii) Nevertheless, its solution qualities are almost equal to those of HLLD, as opposed to very diffused HLL solutions. For benchmark tests, detailed and important flow physics such as multidimensional shock/shock interactions have been successfully reproduced by SLAU2. We hope that SLAU2 will contribute to further progress of the astrophysics and other research fields.

A spatially second-order or higher method is typically employed in practical simulations of FVM. To achieve at least second-order accuracy, the cell-internal distribution of variables should be reconstructed. There are various reconstruction methods such as MUSCL, (Weighted) Least Squares, Green-Gauss, and hybridizations of Green-Gauss/Least Squares, … but which is the best way? The answer depends on the employed numerical setup such as cell geometries and data structure (e.g., whether a structured or unstructured grid is used). In addition to this, a slope limiter such as the minmod limiter or Venkatakrishnan limiter is required to prevent spurious oscillations at discontinuities. This chapter will summarize those reconstruction methods and slope limiters, as well as our recent proposals, including the second limiter and the post limiter.

This chapter will describe the extensions of the AUSM-family fluxes (specifically, SLAU2) to real fluids of multiphase flows, supercritical fluids, and magnetohydrodynamics (MHD), where the governing equations and/or their discretizations differ from those for the perfect gas. These fluids are of great importance to physics and industries, but call for special care due to the changes in the equations. Some readers may wonder why the author appears to have a preference for the AUSM family. Here is a list of primary reasons: 1. They are robust and accurate for resolving shock waves at high speeds. 2. All-speed variants (e.g., AUSM+-up, SLAU2) are available that are applicable to low speeds. 3. No differentiation of a flux function or its Eigenstructure is required, which allows its straightforward application to the complex equation-of-state (EoS) of multiphase flows, supercritical fluids, or MHD.

There are many flux functions available today to obtain the inviscid flux through the cell interface. The idea of treating the cell interface was first proposed by Godunov, who regarded the variable jump there as a Riemann problem. Later, many Godunov-type methods were invented, such as an approximate Riemann solver by Roe, flux vector splitting (FVS) by Steger and Warming or van Leer, its simplified version AUSM (Advection Upstream Splitting Method), and the further modified SLAU (Simple Low-dissipation AUSM) or SLAU2. The Roe flux successfully avoided the iterations required in Godunov’s exact Riemann solver with a reasonable approximation of discontinuities with the “Roe average.” The FVS’s feature is simplicity: it splits waves traveling in the positive (right) and negative (left) directions. Liou further simplified the FVS by treating the mass flux (= convective field) and pressure flux (= acoustic field) separately in AUSM. SLAU is one of its variants extended to low speeds, and SLAU2 greatly enhanced its robustness at high speeds. There is also an HLL (Harten–Lax–van Leer) family which is also popular partly due to its conceptual clarity. In addition, combinations of these methods are, of course, possible. In the following, the flux functions will be explained in two-dimensional forms, unless otherwise stated.

In spite of the (assumed) maturity of compressible CFD technologies today, simulations of a hypersonic flow and a low-speed flow (nearly incompressible flow) are still challenging. The former suffers from anomalous solutions arising from shock capturing (e.g., the carbuncle phenomena). This can be mitigated at least partly by carefully selecting a numerical flux function, a slope limiter, and a computational grid. However, there is no universal scheme that is completely free of those shock anomalies. The latter, the low-speed flow problem, is divided into two subproblems: very slow convergence, known as the “stiffness problem,” and a physically incorrect solution due to huge numerical dissipation. Fortunately, these are known to be avoided if an appropriate combination is adopted for a time integration method and a numerical flux function. In this chapter‚ the current status of these problems is introduced with some actual numerical examples and the author’s explanations based on his experience. The detailed formulations of the numerical algorithms are deferred to the next chapter or simply referred to external sources.

Computational fluid dynamics (CFD) is sometimes regarded as a mature technology. In the author’s opinion, this is only partly correct. The fundamental ideas of CFD such as the finite volume method (FVM) are indeed well established, whereas some classes of problems such as hypersonic heating or real fluid simulations are still challenging, as will be discussed in the subsequent chapters. Thus, we begin this book by reviewing those basics in this chapter, specifically by describing the governing equations (i.e., the Navier–Stokes equations, or equations of mass, momentum, and energy conservation) for compressible flows. They are discretized, for computational purposes, by the FVM, which is the conventional procedure. Through this approximation, the equations are closed along with the equation of state and are valid for every computational element (=cell). In this chapter, only a brief explanation is given of how those equations are numerically solved in the framework of the FVM, using methods such as space reconstruction, slope limiting, flux computation, and time integration. Interested readers, including who have just entered the CFD world, are encouraged to refer to the standard books mentioned in the Preface.

Accepted: 2018-04-01, 資料番号: SA1180197000

Physical characteristics: Original contains color illustrations, Accepted: 2018-04-13, 資料番号: PA1920042000

形態: カラー図版あり, Physical characteristics: Original contains color illustrations, Accepted: 2018-01-07, 資料番号: PA1810057000

SLAU2 (Simple Low-dissipation Advection-Upstream-splitting-method 2) is an approximate Riemann solver belonging to the AUSM family of schemes in gas dynamics. SLAU2 captures shock waves stably in a supersonic range and realizes high resolutions in the low-speed range (Mach number 0.01 or less) by controlling numerical dissipation. In a previous study, this scheme was successfully extended to magnetohydrodynamics (MHD) simulations, such as SLAU2-HLL (SLAU2-Harten–Lax–van Leer). However, the present study reveals that SLAU2-HLL exhibits unphysical oscillations in low-speed MHD tests. This problem has been found to be caused by insufficient numerical dissipation at the magnetic field discontinuity in a low speed range; thus, we recover the numerical dissipation only where necessary by introducing a wiggle sensor function to the pressure flux part of SLAU2-HLL. This change has enabled SLAU2-HLL to calculate low-speed MHD without unphysical oscillations. Furthermore, we constructed SLAU2-HLLD hybridized with HLLD (HLL-Discontinuity), instead of HLL, which can handle Alfven waves. By combining this change with the wiggle-sensing stabilization method, we have succeeded in improving the stability and resolution for low Mach MHD flows from the original SLAU2-HLL. The effect of the modification is demonstrated using one- and two-dimensional numerical examples.

形態: カラー図版あり, Physical characteristics: Original contains color illustrations, Accepted: 2017-04-01, 資料番号: PA1820013000

Accepted: 2017-03-22, 資料番号: SA1170191000

Advection upstream splitting method (AUSM) and Harten‐Lax‐van Leer with contact (HLLC) are two popular families of flux functions. The AUSM is simple and requires no eigenstructure, which facilitates its extensions to general equations of state. Furthermore, one of its variants, simple low‐dissipation AUSM (SLAU), is applicable to all speeds and features removal of parameter setting by the user. HLLC, on the other hand, clearly defines three distinct waves in Riemann problem, namely, left‐running and right‐running acoustic waves, and entropy wave. This paper demonstrates that HLLC can be written in a very similar form with the AUSM family and that the similar manner in extending AUSM family to all speeds is easily incorporated into HLLC in this AUSM‐like form. Then, we combine the strengths of the both flux functions and offer a new inviscid numerical flux function within the framework of monotone upwind scheme for conservation laws (MUSCL) in computational fluid dynamics (CFD) for Euler and Navier‐Stokes equations. The resultant HLLC with low dissipation (HLLCL) numerical flux can compute low Mach number flows and sound propagations at the same time with high accuracy, as demonstrated by one‐dimensional and two‐dimensional numerical examples. Furthermore, the results indicate that its extensions to general fluids such as supercritical fluids are encouraging., This is the peer reviewed version of the following article: [Kitamura et Shima, 2019, International journal for numerical methods in fluids], which has been published in final form at [https://doi.org/10.1002/fld.4782]. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions.

In this paper, we present Synesthesia Wear, a full-body, customizable haptic interface, and demonstrate its capabilities with an untethered spatial computing experience. This wear not only looks as flexible as ordinary cloth, but also the attached modules are powered and controlled through this conductive textile via two-dimensional signal transmission(2DST) technology. The haptic modules have a pin, badge-like connector, and it can be freely attached on the conductive textile(Fig. 1(b)), enabling users to personally customize the experience to their own liking. This module can render variations of haptic feedback to the torso and all limbs of the body, and visualize representations using LED light patterns. We also designed a spatial computing experience(Fig. 1(c)) inspired by the perceptual phenomenon called synesthesia. The system provides an sensory blended experience in which the user walks around freely in real space. The user can interact with real and virtual environments, in a reality-overlapping way by wearing Synesthesia Wear.

The concept of spatial computing has a high potential to augment our lives. We can imagine the expansion of the concept of spatial computing in the future as the expanded visual space will blend into our daily lives. In such a future, how do we feel and interact with another reality that overlaps with real space? We have researched this question from an approach using a haptic interface. We previously developed the Synesthesia Suit[Konishi et al. 2016]. This is a full body haptic suit that extends the VR experience of the game "Rez Infinite". It delivers the visual and musical experience of "Rez" to the whole body, and provides haptic feedback. However, the Synesthesia Suit is difficult to walk around in a physical space, due to the thick cables required for its operation. Basically it is especially suited for VR gaming and it was difficult to apply to spatial computing experience.