Turbulent Shock Research Articles

Decaying vortex and wave turbulence in rotating shallow water model, as follows from high-resolution direct numerical simulations

We report results of direct numerical simulations of decaying turbulence in an inviscid rotating shallow water model. We use a new-generation high-resolution well-balanced shock-capturing finite-volume scheme with several types of initializations: “classical” ones with random velocity and/or height fields, or an initialization with randomly oriented coherent vortex dipoles. Together with “full” turbulence simulations we also perform pure wave-turbulence ones, starting from an initial random wave field of small amplitude with zero potential vorticity anomaly and a given initial spectrum. Statistical properties of the rotating shallow water turbulence, as well as the development of coherent structures and their interactions are studied in detail. For all “full” turbulence simulations we find a tendency to form coherent structures with clear cyclone-anticyclone asymmetry and very steep energy spectra, with exponents close to −6. We also observe a decorrelation of the vortex and wave fields in time, even at significant Rossby numbers. However, we do not observe a universal power law in the evolution of coherent vortices, predicted by the “universal decay” theory for the 2D turbulence. A clear sensitivity to the initial conditions is thus established. For wave-turbulence simulations we observe a tendency to form very steep spectra different from the predictions of the so-called weak turbulence, and of both the turbulence of cusped nonlinear waves and the shock turbulence.

Numerical experiments on magnetic reconnection in solar flare and coronal mass ejection current sheets

Magnetic reconnection plays a critical role in energy conversion during solar eruptions. This paper presents a set of magnetohydrodynamic experiments for the magnetic reconnection process in a current sheet (CS) formed in the wake of the rising flux rope. The eruption results from the loss of equilibrium in a magnetic configuration that includes a current-carrying flux rope, representing a pre-existing filament. In order to study the fine structure and micro processes inside the CS, mesh refinement is used to reduce the numerical diffusion. We start with a uniform, explicitly defined resistivity which results in a Lundquist number S = 10(4) in the vicinity of CS. The use of mesh refinement allows the simulation to capture high-resolution features such as plasmoids from the tearing mode and plasmoid instability regions of turbulence and slow-mode shocks. Inside the CS, magnetic reconnection goes through the Sweet-Parker and the fractal stages, and eventually displays a time-dependent Petschek pattern. Our results support the concept of fractal reconnection suggested by Shibata et al. and Shibata & Tanuma, and also suggest that the CS evolves through Sweet-Parker reconnection prior to the fast reconnection stage. For the first time, the detailed features and/or fine structures inside the coronal mass ejection/flare CS in the eruption were investigated in this work.

The Acceleration Mechanism of Anomalous Cosmic Rays

This paper reviews our current understanding of the acceleration mechanism of anomalous cosmic rays (ACRs). ACRs were first discovered in the early 1970s and soon afterwards it was recognized that they were accelerated interstellar pickup ions that obtained most of their energization in the outer heliosphere. Their observed composition and charge state suggest they are accelerated to over 200 MeV total energy in about a year. Diffusive shock acceleration at the solar-wind termination shock, which provided a natural explanation for spacecraft observations prior to the Voyager crossings of the termination shock in 2004 and 2007, was the long-held paradigm for the acceleration mechanism. But when both Voyagers crossed the shock, the ACR energy spectrum remained modulated, suggesting a source more distant than the shock. While shock acceleration remains a popular mechanism, other ideas have emerged recently to explain the observations. This review focuses on three main acceleration mechanisms that have been proposed: (a) acceleration at the termination shock including new effects such as the global blunt-shape of the shock and large-scale turbulence, (b) acceleration by magnetic reconnection in the heliosheath, and (c) acceleration by diffusive compression acceleration in the heliosheath.

A STUDY OF HEATING AND COOLING OF THE ISM IN NGC 1097 WITHHERSCHEL-PACS ANDSPITZER-IRS

NGC 1097 is a nearby Seyfert 1 galaxy with a bright circumnuclear starburst ring, a strong large-scale bar and an active nucleus. We present a detailed study of the spatial variation of the far infrared (FIR) [CII]158um and [OI]63um lines and mid-infrared H2 emission lines as tracers of gas cooling, and of the polycyclic aromatic hydrocarbon (PAH) bands as tracers of the photoelectric heating, using Herschel-PACS, and Spitzer-IRS infrared spectral maps. We focus on the nucleus and the ring, and two star forming regions (Enuc N and Enuc S). We estimated a photoelectric gas heating efficiency ([CII]158um+[OI]63um)/PAH in the ring about 50% lower than in Enuc N and S. The average 11.3/7.7um PAH ratio is also lower in the ring, which may suggest a larger fraction of ionized PAHs, but no clear correlation with [CII]158{\mu}m/PAH(5.5 - 14um) is found. PAHs in the ring are responsible for a factor of two more [CII]158um and [OI]63um emission per unit mass than PAHs in the Enuc S. SED modeling indicates that at most 25% of the FIR power in the ring and Enuc S can come from high intensity photodissociation regions (PDRs), in which case G0 ~ 10^2.3 and nH ~ 10^3.5 cm^-3 in the ring. For these values of G0 and nH PDR models cannot reproduce the observed H2 emission. Much of the the H2 emission in the starburst ring could come from warm regions in the diffuse ISM that are heated by turbulent dissipation or shocks.

Discovery of interstellar mercapto radicals (SH) with the GREAT instrument on SOFIA

We report the first detection of interstellar mercapto radicals, obtained along the sight-line to the submillimeter continuum source W49N. We have used the GREAT instrument on SOFIA to observe the 1383 GHz Doublet Pi 3/2 J = 5/2 - 3/2 lambda doublet in the upper sideband of the L1 receiver. The resultant spectrum reveals SH absorption in material local to W49N, as well as in foreground gas, unassociated with W49N, that is located along the sight-line. For the foreground material at velocities in the range 37 - 44 km/s with respect to the local standard of rest, we infer a total SH column density ~ 2.6 E+12 cm-2, corresponding to an abundance of ~ 7 E-9 relative to H2, and yielding an SH/H2S abundance ratio ~ 0.13. The observed SH/H2S abundance ratio is much smaller than that predicted by standard models for the production of SH and H2S in turbulent dissipation regions and shocks, and suggests that the endothermic neutral-neutral reaction SH + H2 -> H2S + H must be enhanced along with the ion-neutral reactions believed to produce CH+ and SH+ in diffuse molecular clouds.

Dynamic -equation model for large-eddy simulation of compressible flows

AbstractThis paper presents a dynamic one-equation eddy viscosity model for large-eddy simulation (LES) of compressible flows. The transport equation for subgrid-scale (SGS) kinetic energy is introduced to predict SGS kinetic energy. The exact SGS kinetic energy transport equation for compressible flows is derived formally. Each of the unclosed terms in the SGS kinetic energy equation is modelled separately and dynamically closed, instead of being grouped into production and dissipation terms, as in the Reynolds averaged Navier–Stokes equations. All of the SGS terms in the filtered total energy equation are found to reappear in the SGS kinetic energy equation. Therefore, these terms can be included in the total energy equation without adding extra computational cost.A prioritests using direct numerical simulation (DNS) of decaying isotropic turbulence show that, for a Smagorinsky-type eddy viscosity model, the correlation between the SGS stress and the model is comparable to that from the original model. Also, the suggested model for the pressure dilatation term in the SGS kinetic energy equation is found to have a high correlation with its actual value. Ina posterioritests, the proposed dynamic$k$-equation model is applied to decaying isotropic turbulence and normal shock–isotropic turbulence interaction, and yields good agreement with available experimental and DNS data. Compared with the results of the dynamic Smagorinsky model (DSM), the$k$-equation model predicts better energy spectra at high wavenumbers, similar kinetic energy decay and fluctuations of thermodynamic quantities for decaying isotropic turbulence. For shock–turbulence interaction, the$k$-equation model and the DSM predict similar evolutions of turbulent intensities across shocks, owing to the dominant effect of linear interaction. The proposed$k$-equation model is more robust in that local averaging over neighbouring control volumes is sufficient to regularize the dynamic procedure. The behaviour of pressure dilatation and dilatational dissipation is discussed through the budgets of the SGS kinetic energy equation, and the importance of the dilatational dissipation term is addressed.

CONNECTING THE SUN AND THE SOLAR WIND: THE FIRST 2.5-DIMENSIONAL SELF-CONSISTENT MHD SIMULATION UNDER THE ALFVÉN WAVE SCENARIO

The solar wind emanates from the hot and tenuous solar corona. Earlier studies using 1.5 dimensional simulations show that Alfv\'{e}n waves generated in the photosphere play an important role in coronal heating through the process of non-linear mode conversion. In order to understand the physics of coronal heating and solar wind acceleration together, it is important to consider the regions from photosphere to interplanetary space as a single system. We performed 2.5 dimensional, self-consistent magnetohydrodynamic simulations, covering from the photosphere to the interplanetary space for the first time. We carefully set up the grid points with spherical coordinate to treat the Alfv\'{e}n waves in the atmosphere with huge density contrast, and successfully simulate the solar wind streaming out from the hot solar corona as a result of the surface convective motion. The footpoint motion excites Alfv\'{e}n waves along an open magnetic flux tube, and these waves traveling upwards in the non-uniform medium undergo wave reflection, nonlinear mode conversion from Alfv\'{e}n mode to slow mode, and turbulent cascade. These processes leads to the dissipation of Alfv\'{e}n waves and acceleration of the solar wind. It is found that the shock heating by the dissipation of the slow mode wave plays a fundamental role in the coronal heating process whereas the turbulent cascade and shock heating drive the solar wind.

Ultraviolet absorption observations of intermediate-velocity cloud gas detected towards the M 15 globular cluster

Aims. We present medium resolution ultraviolet interstellar absorption measurements recorded with the HST-COS and FUSE spectrographs towards two post-AGB stars (K 559 & K 648) located within the M 15 globular cluster (l ∼ 65 ◦ , b ∼ –27 ◦ ). By sampling interstellar gas over the 10.4 kpc sight-line towards M 15 we wish to reveal spectral features that are associated with absorption due to the foreground g1 intermediate velocity cloud (IVC), whose distance has previously been constrained to lie between 1.8–3.8 kpc. Methods. Inspection of the UV line profiles recorded towards both stars have revealed measurable IVC absorption at Vlsr ∼ +61.5 ± 5k m s −1 in the profiles of the CI, CII, CII*, CIV, NI, NII, OI, OVI, AlII, SiII, SiIII, SiIV, PII, SII, FeII, FeIII and NiII ions. Line-profile fitting to the IVC absorption features has resulted in column density determinations for the low and high ions. The best-fit column density values for the various ions have near identical values along both sight-lines, such that our UV data does not reveal the significant small-scale structure that has been reported previously for the g1 cloud. Results. The observed column density ratios of the CIV, SiIV, OVI and NV IV components are consistent with what may be expected from turbulent mixing layers, shock ionization or halo SNR models, although no one model can predict all of the observed ratios. We derive sub-solar metallicity values of [O/H] = −1.22 ± 0.44 and [N/H] = −1.21 ± 0.38 for the neutral IVC gas, and also the IV components of C, Si, Al, Ni and Fe mainly possess less than solar abundance ratios relative to that of N. A possible origin for the g1 IVC is that of a low metallicity cloud that has been accreted towards our galaxy, has passed through the disk and is now moving away from the galactic plane.

Experimental investigation of shock structure in turbulent Coanda jets

Although Coanda surfaces are extremely useful for applications in industrial exhaust, the generation of noise in supersonic flows around such surfaces is not well understood. In order to effectively engineer a solution to this noise problem, the noise generation must be able to be accurately modeled. The two dominating generators of sound are turbulent mixing noise and shock associated noise (SAN). The first step necessary to model SAN is a precise predictor of the shock structure within the jet. A MATLAB algorithm is developed to translate Schlieren photos of the flow into qualitative shock location data. This data will be used in conjunction with the method of characteristics to create a model which predicts shock location around a Coanda surface for several slot widths and exit pressures.

Multiphase High-Velocity Gas Detected within 7 kpc Toward the M13 Globular Cluster

ABSTRACTWe present medium-resolution ultraviolet interstellar absorption measurements recorded with the HST-COS and FUSE spectrographs toward the post-AGB star Barnard 29 in the M13 globular cluster. Inspection of the UV spectra has revealed absorption at in the absorption profiles of the C I, C II, , C IV, N I, N II, N V, O I, ALII, Si II, Si IV, S II and Fe II ions. This component can be associated with an intermediate-velocity cloud (IVC), previously identified by both radio and visible observations. More importantly, these data have newly revealed high-velocity absorption at VLSR = -121 ± 3 km s-1 in the UV ions of C II, C III, C IV, N II, Si II, and Si IV. This absorption is thought to arise in a highly ionized, multiphase high-velocity cloud (HVC) located a distance of 0.46 < z < 4.7 kpc and has no measurable counterpart in the 21 cm neutral H I emission profile or the normal tracers of neutral gas in the ISM such as Na I, N I or O I. This makes it one of the four nearest highly ionized HVCs yet discovered. The observed column density ratios of the H V components to the C IV and Si IV lines are consistent with values predicted for a turbulent mixing layer or shock ionization of a gas cloud. We have derived estimates of the abundance ratios of C and Si with respect to N relative to their corresponding solar values. Our results indicate values of [Si/N] > +0.40 ± 0.21 and [C/N] = +0.10 ± 0.25 for the HVC gas component. These values indicate that the H V gas has higher than solar relative abundances, consistent with gas of a supersolar metallicity. Several other highly ionized HVCs with distances of less than 7.5 kpc have recently been shown to possess similarly high-metallicity values that are consistent with an origin in condensing returning gas from a galactic fountain.

The role of the induction zone on the detonation–turbulence linear interaction

Detonation–turbulence linear interaction analysis extends the non-reactive shock–turbulence analog by considering geometrical scaling of the noise with respect to the half-reaction distance. The analysis emphasizes the effect of structure in energizing selective frequencies, and determining acoustic amplification in the farfield. Natural frequencies are determined as eigenvalues of the inviscid non-forced interaction problem. They modify postshock energy spectra by supporting resonant amplification, and cast light on the role of the activation energy on the detonation–turbulence interaction. Detonations with higher activation energies amplify smaller scales by resonant amplification. An analysis of the bifurcation parameters reveals a strong link between detonation overdrive and acoustic attenuation. The damping is correlated with the subcritical nature of the characteristic solutions for high overdrives. For detonation conditions on the stability boundary, a larger overdrive supports a weaker resonant peak in both the temperature and longitudinal velocity spectra. Postshock temperature variances feature a well-defined maximum within the reaction zone, which is found to be sensitive to changes in detonation structure.

Molecular Tracers of Turbulent Shocks in GMCs

Molecular Tracers of Turbulent Shocks in GMCs

Reynolds-averaged Navier–Stokes model predictions of linear instability. II. Shock-driven flows

Applying the formalism for buoyancy- and shear-driven instabilities developed in Paper I [B.M. Johnson and O. Schilling, J. Turbul. 12(36) (2011), pp. 1–38], it is shown here that Reynolds-averaged Navier–Stokes (RANS) models describe the early phase of shock-driven instabilities: the amplification of velocity fluctuations due to the passage of a shock for shock–turbulence interaction and the initial deposition of solenoidal velocity at an interface by a shock for the Richtmyer–Meshkov instability. The correspondence between the closed RANS equations in the absence of turbulent diffusion and the unclosed RANS equations under the assumptions of linear theory discussed in Paper I is shown here to extend to shock-driven flows. In order to compare the models with linear theory, a form of linear interaction analysis appropriate for short-wavelength perturbations is developed and applied to a shock interacting with an ambient velocity field. It is shown that relaxing Morkovin's hypothesis can result in arbitrarily large amplification of ambient velocity fluctuations due to the passage of a shock. The classical Richtmyer–Meshkov instability corresponds to the case in which the amplification is formally infinite as the initial velocity fluctuation is zero. The solutions obtained here for both the K-ε and K-ℓ models provide insight into the choice of appropriate initial conditions for RANS models, impose various constraints on the model coefficients and can be used to verify numerical discretizations of the model equations. The analysis also quantifies and addresses issues regarding convergence under grid refinement in the presence of shocks: it is shown that convergence in a shock-driven flow can be improved by scaling the initial length scale with the grid spacing.

Reynolds-averaged Navier–Stokes model predictions of linear instability. I: Buoyancy- and shear-driven flows

Reynolds-averaged Navier–Stokes (RANS) models based on turbulent kinetic energy and dissipation rate or length scale transport equations are commonly used for fully developed turbulence arising from buoyancy, shear, or shocks. It is shown here that RANS models also describe the linear instability phase for buoyancy instabilities (specifically, the Rayleigh–Taylor instability) and shear instabilities (specifically, the Kelvin–Helmholtz instability and stratified shear flow). During the initial phases of the evolution of these models, turbulent diffusion is negligible, the fluctuation energy grows exponentially with negligible coupling to the mean flow, and the model coefficients can be chosen such that the growth rate is equivalent to the physical growth rate of short-wavelength perturbations. The reduced equations obtained by neglecting turbulent diffusion correspond to the unclosed RANS equations under the assumptions of linear theory (i.e., retaining only second-order correlations). The correspondence with linear theory requires interpreting the model length scale as a Lagrangian fluid displacement rather than a quantity derived from the turbulent kinetic energy dissipation rate. The analytical solutions obtained for both the K-ε and K-ℓ models in the absence of diffusion provide insight into the choice of appropriate initial conditions for RANS models, impose various constraints on the model coefficients, and can be used to verify numerical discretizations of the model equations. The analysis also quantifies and addresses issues regarding convergence under grid refinement in the presence of discontinuous mean flows. Paper II [B.M. Johnson and O. Schilling, Reynolds-averaged Navier–Stokes model predictions of linear instability. II: Shock- driven flows, J. Turbul. 12(33) (2011), pp. 1–31] applies the analysis developed herein to shock–turbulence interaction and the Richtmyer–Meshkov instability.

A turbulent mixing Reynolds stress model fitted to match linear interaction analysis predictions

To predict the evolution of turbulent mixing zones developing in shock tube experiments with different gases, a turbulence model must be able to reliably evaluate the production due to the shock–turbulence interaction. In the limit of homogeneous weak turbulence, ‘linear interaction analysis’ (LIA) can be applied. This theory relies on Kovasznay's decomposition and allows the computation of waves transmitted or produced at the shock front. With assumptions about the composition of the upstream turbulent mixture, one can connect the second-order moments downstream from the shock front to those upstream through a transfer matrix, depending on shock strength. The purpose of this work is to provide a turbulence model that matches LIA results for the shock–turbulent mixture interaction. Reynolds stress models (RSMs) with additional equations for the density–velocity correlation and the density variance are considered here. The turbulent states upstream and downstream from the shock front calculated with these models can also be related through a transfer matrix, provided that the numerical implementation is based on a pseudo-pressure formulation. Then, the RSM should be modified in such a way that its transfer matrix matches the LIA one. Using the pseudo-pressure to introduce ad hoc production terms, we are able to obtain a close agreement between LIA and RSM matrices for any shock strength and thus improve the capabilities of the RSM.

Direct numerical simulation of transitional flow at high Mach number coupled with a thermal wall model

In transitional and turbulent high speed boundary-layer flows the wall thermal boundary conditions play an important role and in many cases an assumption of a constant temperature or a specified heat flux may not be appropriate for numerical simulations. In this paper we extend a formulation for direct numerical simulation of compressible flows to include a thin plate that is thermally fully coupled to the flow. Even without such thermal coupling compressible flows with shock waves and turbulence represent a challenge for numerical methods. In this paper we review the scaling properties of algorithms, based on explicit high-order finite differencing combined with shock capturing, that are suitable for dealing with such flows. An application is then considered in which an isolated roughness element is of sufficient height to trigger transition in the presence of acoustic forcing. With the thermal wall model included it is observed that the plate heats up sufficiently during the simulation for the transition process to be halted and the flow consequently re-laminarises.

Cosmic ray current driven turbulence in shocks with efficient particle acceleration: the oblique, long-wavelength mode instability

In order for diffusive shock acceleration (DSA) to accelerate particles to high energies, the energetic particles must be able to interact with magnetic turbulence over a broad wavelength range. The weakly anisotropic distribution of accelerated particles, i.e., cosmic rays (CRs), is believed capable of producing this turbulence in a symbiotic relationship where the magnetic turbulence required to accelerate the CRs is created by the accelerated CRs themselves. In efficient DSA, this wave-particle interaction can be strongly nonlinear where CRs modify the plasma flow and the specific mechanisms of magnetic field amplification. Resonant interactions have long been known to amplify magnetic fluctuations on the scale of the CR gyroradius, and Bell (2004) showed that the CR current can efficiently amplify magnetic fluctuations with scales smaller than the CR gyroradius. Here, we show with a multi-scale, quasi-linear analysis that the presence of turbulence with scales shorter than the CR gyroradius enhances the growth of modes with scales longer than the gyroradius, at least for particular polarizations. We use a mean-field approach to average the equation of motion and the induction equation over the ensemble of magnetic field oscillations accounting for the anisotropy of relativistic particles on the background plasma. We derive the response of the magnetized CR current on magnetic field fluctuations and show that, in the presence of short-scale, Bell-type turbulence, long wavelength modes are amplified. The polarization, helicity, and angular dependence of the growth rates are calculated for obliquely propagating modes for wavelengths both below and above the CR mean free path. The long wavelength growth rates we estimate for typical supernova remnant parameters are sufficiently fast to suggest a fundamental increase in the maximum CR energy a given shock can produce.

Particle acceleration in Blazars

AbstractUnderstanding the variable emission of blazars observed with gamma-ray telescopes and Fermi has become a major challenge for theoretical models of particle acceleration. Here, we introduce a novel time-dependent emission model in which the maximum energy of particles is determined from a balance between Fermi type I and II acceleration energy gains and radiative energy losses, allowing for an explanation of both the characteristic spectral energy distribution of blazars and their intrinsic sub-hour variability. Additionally, we can determine the physical condition of the emitting plasma concerning its turbulence and typical shock speeds.

Postshock turbulence and diffusive shock acceleration in young supernova remnants

<i>Context. <i/>Thin X-ray filaments are observed in the vicinity of young supernova remnants (SNR) blast waves. Identifying the process that creates these filaments would provide direct insight into the particle acceleration occurring within SNR and in particular the cosmic ray yield.<i>Aims. <i/>We investigate magnetic amplification in the upstream medium of a SNR blast wave through both resonant and non-resonant regimes of the streaming instability. We attempt to understand more clearly of the diffusive shock acceleration (DSA) efficiency by considering various relaxation processes of the magnetic fluctuations in the downstream medium. Multiwavelength radiative signatures originating in the SNR shock wave are used to test various downstream turbulence relaxation models.<i>Methods. <i/>Analytical and numerical calculations that couple stochastic differential equation schemes with 1D spherical magnetohydrodynamics simulations are used to investigate, in the context of test particles, turbulence evolution in both the forshock and post-shock regions. Stochastic second-order Fermi acceleration induced by resonant modes, magnetic field relaxation and amplification, and turbulence compression at the shock front are considered to model the multiwavelength filaments produced in SNRs. The <i>γ<i/>-ray emission is also considered in terms of inverse Compton mechanism.<i>Results. <i/>We confirm the result of Parizot and collaborators that the maximum CR energies should not go well beyond PeV energies in young SNRs where X-ray filaments are observed. To reproduce observational data, we derive an upper limit to the magnetic field amplitude and so ensure that stochastic particle reacceleration remains inefficient. Considering various magnetic relaxation processes, we then infer two necessary conditions to achieve efficient acceleration and X-ray filaments in SNRs: (1) the turbulence must fulfil the inequality 2 - <i>β<i/> - <i>≥<i/> 0; where <i>β<i/> is the turbulence spectral index and is the relaxation length energy power-law index; (2) the typical relaxation length must be of the order the X-ray rim size. We find that Alvénic/fast magnetosonic mode damping fulfils all conditions; while non-linear Kolmogorov damping does not. By confronting previous relaxation processes with observational data, we deducte that among our SNR sample, data for the older ones (SN1006 and G347.3-0.5) does not comply with all conditions, which means that their X-ray filaments are probably controlled by radiative losses. The younger SNRs, Cassiopeia A, Tycho, and Kepler pass all tests and we infer that the downstream magnetic field amplitude is in the range of 200–300 <i>μ<i/>Gauss.

On high-order shock-fitting and front-tracking schemes for numerical simulation of shock–disturbance interactions

High-order methods that can resolve interactions of flow-disturbances with shock waves are critical for reliable numerical simulation of shock wave and turbulence interaction. Such problems are not well understood due to the limitations of numerical methods. Most of the popular shock-capturing methods are only first-order accurate at the shock and may incur spurious numerical oscillations near the shock. Shock-fitting algorithms have been proposed as an alternative which can achieve uniform high-order accuracy and can avoid possible spurious oscillations incurred in shock-capturing methods by treating shocks as sharp interfaces. We explore two ways for shock-fitting: conventional moving grid set-up and a new fixed grid set-up with front tracking. In the conventional shock-fitting method, a moving grid is fitted to the shock whereas in the newly developed fixed grid set-up the shock front is tracked using Lagrangian points and is free to move across the underlying fixed grid. Different implementations of shock-fitting methods have been published in the literature. However, uniform high-order accuracy of various shock-fitting methods has not been systematically established. In this paper, we carry out a rigorous grid-convergence analysis on different variations of shock-fitting methods with both moving and fixed grids. These shock-fitting methods consist of different combinations of numerical methods for computing flow away from the shock and those for computing the shock movement. Specifically, we consider fifth-order upwind finite-difference scheme and shock-capturing WENO schemes with conventional shock-fitting and show that a fifth-order convergence is indeed achieved for a canonical one-dimensional shock-entropy wave interaction problem. We also show that the method of finding shock velocity from one characteristic relation and Rankine–Hugoniot jump condition performs better than the other methods of computing shock velocities. A high-order front-tracking implementation of shock-fitting is also presented in this paper and nominal rate of convergence is shown. The front-tracking results are validated by comparing to results from the conventional shock-fitting method and a linear-interaction analysis for a two-dimensional shock disturbance interaction problem.