
[Sponsors] 
Publication date: Available online 18 February 2021
Source: Computers & Fluids
Author(s): Z.J. Wang, Salman Rahmani
Publication date: Available online 18 February 2021
Source: Computers & Fluids
Author(s): T. Mukha, R.E. Bensow, M. Liefvendahl
Publication date: Available online 18 February 2021
Source: Computers & Fluids
Author(s): Youming Tai, Tomoaki Watanabe, Koji Nagata
Publication date: Available online 23 February 2021
Source: Computers & Fluids
Author(s): Geng Liu, Taehun Lee
Publication date: Available online 23 February 2021
Source: Computers & Fluids
Author(s): Lina Baroudi, Taehun Lee
Publication date: 30 March 2021
Source: Computers & Fluids, Volume 218
Author(s): Edoardo Saredi, Nikhilesh Tumuluru Ramesh, Andrea Sciacchitano, Fulvio Scarano
Publication date: 30 March 2021
Source: Computers & Fluids, Volume 218
Author(s):
Publication date: Available online 17 February 2021
Source: Computers & Fluids
Author(s): Mohamad Sadeq Karimi, Mehrdad Raisee, Mohamed Farhat, Patrick Hendrick, Ahmad Nourbakhsh
Publication date: Available online 17 February 2021
Source: Computers & Fluids
Author(s): Vikram Singh, Steven Frankel, Jan Nordström
Publication date: Available online 12 January 2021
Source: Computers & Fluids
Author(s): Mohammed Rammane, Said Mesmoudi, Abdeljalil Tri, Bouazza Braikat, Noureddine Damil
In this paper, we present consistent and inconsistent discontinous Galerkin methods for incompressible Euler and Navier‐Stokes equations with the kinematic pressure, Bernoulli function and EMAC function. Semiand fully discrete energy stability of the proposed dG methods are proved in a unified fashion. Conservation of total energy, linear and angular momentum is discussed with both central and upwind uxes. Numerical experiments are presented to demonstrate our findings and compare our schemes with conventional schemes in the literature in both unsteady and steady problems. Numerical results show that global conservation of the physical quantities may not be enough to demonstrate the performance of the schemes, and our schemes are competitive and able to capture essential physical features in several benchmark problems.
Boundary integral methods are highly suited for problems with complicated geometries, but require special quadrature methods to accurately compute the singular and nearly singular layer potentials that appear in them. This paper presents a boundary integral method that can be used to study the motion of rigid particles in three dimensional periodic Stokes flow with confining walls. A centerpiece of our method is the highly accurate special quadrature method, which is based on a combination of upsampled quadrature and quadrature by expansion (QBX), accelerated using a precomputation scheme. The method is demonstrated for rodlike and spheroidal particles, with the confining geometry given by a pipe or a pair of flat walls. A parameter selection strategy for the special quadrature method is presented and tested. Periodic interactions are computed using the Spectral Ewald (SE) fast summation method, which allows our method to run in O(n log n) time for n grid points in the primary cell, assuming the number of geometrical objects grows while the grid point concentration is kept fixed.
An Adaptive Fup Collocation Method (AFCM) that is adaptive both in space and time was developed. The method is implicit and resolves all spatial and temporal scales independently to each other. The CPU speedup was up to 5 when compared with classical space adaptive algorithm and up to 37 when compared with nonadaptive finite difference solution.
In this paper, we present a full space‐time Adaptive Fup Collocation Method (AFCM) for solving initial‐boundary value problems with particular application on advection‐dominated advection‐diffusion problems. The spatial adaptive strategy dynamically changes the computational grid at each global time step, while the adaptive time‐marching algorithm uses different local time steps for different collocation points based on temporal accuracy criteria. Contrary to the existing space‐time adaptive methods that are based on explicit temporal discretization and scale‐dependent local time stepping, the presented method is implicit and resolves all spatial and temporal scales independently of each other. This means that smaller local time steps are used only for spatial zones where temporal solution changes are intensive, which are not necessarily the zones with finest spatial discretization. In this manner, the computationally efficient full space‐time adaptive strategy accurately resolves small‐scale features and controls numerical error and spurious oscillations. The efficiency and accuracy of AFCM are verified with some classical one‐ and two‐dimensional benchmark test cases.
A novel block method is used to obtain the solutions for a system of boundary value differential equations that describe the flow and heat transfer in a nanofluid moving over a stretching sheet. A comparison between an actively controlled (AC) and a passively controlled (PC) boundary is considered. The study showed that the method gives good convergence, and both AC and PC conditions give similar results away from surfaces.
This study is an investigation of an exponentially decaying internal heat generation rate and free nanoparticle movement on the boundary layer. The equations describing the hydromagnetic flow and heat transfer in a viscous nanofluid moving over an isothermal stretching sheet are solved using a novel numerical approach. A comparison of flow and heat transfer characteristics between an actively controlled (AC) and a passively controlled (PC) nanoparticle concentration boundary is considered. The boundary value partial differential equations are transformed into a system of ordinary differential equations using similarity transformations. The system of ODEs is solved using a new block method without having to reduce the equivalent system to first‐order equations. The solutions are verified using the spectral local linearization method and further validation of the results is confirmed by comparing the current results, for some limiting cases, with those in existing literature. The solutions obtained using the block method are in good agreement with the solution obtained using the spectral local linearization method. The results are in good agreement with existing findings in previous studies. The solutions obtained using the AC and PC nanoparticle concentration boundary conditions are analyzed.
A Characteristic‐Based Polynomial Pressure Projection (CBP3) stabilization is proposed for the finite element incompressible flow solver using linear triangles or bilinear quadrilaterals. The numerical accuracy, convergence, and choice of parameters are studied by performing computations for incompressible flow benchmarks. Proposed CBP3 stabilization can satisfy the LBB or in‐sup condition without instability issues for triangular and quadrilateral finite elements using equal‐order velocity and pressure interpolation and constant pressure projection.
In this paper, a characteristic‐based polynomial pressure projection (CBP3) scheme is proposed to stabilize finite element method for solving incompressible laminar flow. The characteristic‐Galerkin (CG) method is adopted as the stabilization for convection caused oscillation in CBP3 scheme. The pressure oscillation caused by incompressible constraint is stabilized by the polynomial pressure projection (P3) technique. Proposed scheme is suitable for any element using the equal‐order approximation for velocity and pressure. In this paper, the linear triangular and bilinear quadrilateral elements are adopted. The constant pressure projection is used for triangular elements. The CBP3 formulations for quadrilateral element are derived using both constant and linear pressure projections. Besides, the quasi‐implicit second‐order time stepping is adopted. The verification of CBP3 scheme implementation and validation of CBP3 scheme are accomplished by calculating several benchmarks. The results of CBP3 scheme reveal that the linear pressure projection for quadrilateral element is not appropriate due to its severe pressure oscillation. The well‐agreed results of CBP3 scheme using constant pressure projection demonstrate its good stabilization for FEM to solve both low and relatively high Reynolds number flows.
Achieving high numerical resolution in smooth regions and robustness near discontinuities within a unified framework is the major concern while developing numerical schemes solving hyperbolic conservation laws, for which the essentially non‐oscillatory (ENO) type scheme is a favorable solution. Therefore, an arbitrary‐high‐order ENO‐type framework is designed in this paper. With using a typical five‐point smoothness measurement as the shock‐detector, the present schemes are able to detect discontinuities before spatial reconstructions, and thus more spatial information can be exploited to construct incremental‐width stencils without crossing discontinuities, ensuring ENO property and high‐order of accuracy at the same time. The present shock‐detection procedure is specifically examind for justifying its performance of resolving high‐frequency waves, and a standard metric for discontinuous solutions is also applied for measuring the shock‐capturing error of the present schemes, especially regarding the amplitude error in post‐shock regions. In general, the present schemes provide high‐resolution, and more importantly, the schemes are more efficient compared with the typical WENO schemes since only a five‐point smoothness measurement is applied for arbitrary‐high‐order schemes. Numerical results of canonical test cases also provide evidences of the overall performance of the present schemes.
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This article introduces an efficient numerical scheme for the solution of the Benjamin‐Bona‐Mahony equation. The scheme is fully implicit, and combines high‐order time stepping and a hybridizable discontinuous Galerkin method in space. Implicit time stepping allows for larger time steps, while remaining robust for long‐time simulations. It is shown that the scheme is energy stable, and conserves mass. Computational experiments demonstrate that the scheme is high‐order accurate, robust, and possesses good conservation properties.
This article introduces an efficient numerical scheme for the solution of the Benjamin‐Bona‐Mahony equation. The scheme is fully implicit, and combines high‐order time stepping and a hybridizable discontinuous Galerkin method in space. Implicit time stepping allows for larger time steps, while remaining robust for long‐time simulations. It is shown that the scheme is energy stable, and conserves mass. Computational experiments demonstrate that the scheme is high‐order accurate, robust, and possesses good conservation properties.
RK4‐based Random Phase Shift dealiasing scheme shows excellent numerical accuracy at lesser computational cost for the flows with strong gradients. This scheme displays lesser spurious oscillations using similar computational cost of low‐pass filtering‐based schemes. It works quite remarkably even in under‐resolved conditions and also displays excellent numerical stability during long time simulation. An error norm‐based computational efficiency has been discussed for different dealiasing schemes.
In this paper, the Random Phase Shift Method (RPSM) dealiasing scheme has been developed with the classical fourth‐order explicit Runge‐Kutta (RK4) method. This scheme is implemented in different benchmark problems to verify its numerical accuracy and computational efficiency where strong gradients are present in the solution. The propagation of aliasing errors through the substeps of RK4 is derived to show the existence of the residual aliasing error terms which results in mild smoothing effect without dissipating the small‐scale flow structures. Smoothness and numerical stability in the solutions obtained from the RPSM scheme also remain well preserved even at under‐resolved conditions. Numerical results agree well with the analytical and the computed solutions from previous studies. RPSM scheme shows a slight delay in the formation of numerical singularity for the inviscid flows but the filtering‐based schemes suffer from early blow‐up problem. We observe that this scheme displays better resolving ability than higher‐order exponential smoothing spectral filter scheme in capturing the strong fronts accurately even at just resolved spatial grid resolutions. Three‐dimensional truncation‐based dealiasing scheme, spherical truncation (SPT) shows vortices generated due to the parasitic currents in the solution of the inviscid three‐dimensional Taylor Green (TG) vortex flows. RPSM displays only the accurate isocontours of vortical field at nearly same computational expenses as the SPT scheme.
This article presents a model order reduction method based on one of the deep learning techniques, namely, the recursive neural network LSTM. This method first calculates the DMD or POD modes and their temporal coefficients for the simulated data (snapshots) and then uses an LSTM model to predict the temporal coefficients of the modes. The results show the high accuracy of the proposed model for predicting the temporal coefficients on the snapshots of Kelvin‐Helmholtz instability and mass diffusion problems.
In many real‐world applications, mathematical models are highly complex, and numerical simulations in high‐dimensional systems are challenging. Model order reduction is a useful method to obtain a reasonable approximation by significantly reducing the computational cost of such problems. Deep learning technology is a recent improvement in artificial neural networks that can find more hidden information from the data. Deep learning has the advantage of processing data in its raw form and trains the nonlinear system with different levels of representation and predicts the data. In this article, a reduced order model framework based on a combination of deep learning [long short‐term memory (LSTM)] and proper orthogonal decomposition/dynamic mode decomposition (POD/DMD) modes is presented. Due to the robustness and stability of the LSTM recurrent neural network in predicting chaotic dynamical systems, we consider LSTM architecture to develop our data‐driven reduced order modeling (ROM). We investigate the proposed method performance by solving two well‐known canonical cases: a steady shear flow exhibiting the Kelvin‐Helmholtz instability, and two‐dimensional and unsteady mass diffusion equation. The focus of this article is to use LSTM deep recursive neural network to learn the time dynamics and POD/DMD to generate the order reduction model. The results show that the proposed method is very accurate in predicting time dynamics and input reconstruction.
In order to solve incompressible, nonideal MHD, free‐surface flows, two weakly compressible smoothed particle hydrodynamics models with and without the consideration of magnetic induction are proposed. A novel SPH formulation for magnetic induction magnetohydrodynamics is proposed for incompressible free‐surface MHD flows with boundaries with arbitrary electric conductivity. An SPH implementation using the inductionless approximation is also proposed for both electrically conductive and insulating boundaries, in which a Poisson equation is solved to compute the Lorentz force.
In order to solve incompressible, nonideal magnetohydrodynamic (MHD) free‐surface flows, two weakly compressible smoothed particle hydrodynamics models, with and without the consideration of magnetic induction, are developed. The SPH formulation for magnetic induction magnetohydrodynamics (SPMHD), which is popular in astrophysical studies, is applied for the first time to incompressible free‐surface MHD flows, such as liquid metal flows, with the consideration of nonideal MHD effects and boundaries with arbitrary electric conductivity. An SPMHD implementation using the inductionless approximation is also proposed for both electrically conductive and insulating boundaries, in which a Poisson equation is solved to compute the Lorentz force instead of evolving the magnetic induction equation. Both proposed methods are validated against MHD benchmarks, including free‐surface MHD cases. The proposed inductionless SPMHD implementation has the advantages of stability and relaxed time‐step restrictions, but is only accurate at a low range of Hartmann numbers. For high Hartmann number problems, magnetic induction SPMHD model is more accurate. The computational efficiency and conservation error of the two models are compared and discussed.
Publication date: 15 May 2021
Source: Journal of Computational Physics, Volume 433
Author(s): Yabin Zhang, Adrianna Gillman
Publication date: 15 May 2021
Source: Journal of Computational Physics, Volume 433
Author(s): Wanli Wang, Cheng Wang, Tonghui Yang, Dongping Chen
Publication date: Available online 23 February 2021
Source: Journal of Computational Physics
Author(s): Nikita Afanasiev, Vasily Goloviznin
Publication date: Available online 23 February 2021
Source: Journal of Computational Physics
Author(s): Xuelei Lin, Michael K. Ng, Yajing Zhi
Publication date: Available online 23 February 2021
Source: Journal of Computational Physics
Author(s): S. Clain, D. Lopes, R.M.S. Pereira
Publication date: 15 May 2021
Source: Journal of Computational Physics, Volume 433
Author(s): Xiaoyu Mao, Vaibhav Joshi, Rajeev Jaiman
Publication date: 15 May 2021
Source: Journal of Computational Physics, Volume 433
Author(s): Ramakrishnan Thirumalaisamy, Nishant Nangia, Amneet Pal Singh Bhalla
Publication date: 15 May 2021
Source: Journal of Computational Physics, Volume 433
Author(s): Luca Cirrottola, Mario Ricchiuto, Algiane Froehly, Barbara Re, Alberto Guardone, Giuseppe Quaranta
Publication date: 15 May 2021
Source: Journal of Computational Physics, Volume 433
Author(s): Wenrui Hao, Pengtao Sun, Jinchao Xu, Lian Zhang
Publication date: 15 May 2021
Source: Journal of Computational Physics, Volume 433
Author(s): Yi Zhang, Joël Fisser, Marc Gerritsma
In this paper, experimental and numerical methods are presented to investigate the dambreak flow in a horizontal rectangular section flume. In the experimental part of the research, different configurations have been tested: dry flume and the presence of shallow ambient water downstream with varied depth. In addition, experiments with viscosity changes in the fluid have been conducted. Numerically, the volume of the fluid method associated with the shearstress transport turbulence model was used to examine the dambreak flow dynamics. Based on a review of analytical models in the literature, formulas for free water surfaces and propagation fronts were detailed. Qualitatively, various experimental snapshots of free water surfaces were obtained from the digitized images and compared with numerical predictions. Typical jetlike and mushroomlike formations have been observed. Experimental free surface profiles have been plotted against analytical and numerical results for different flow stages. The simulation of highviscous fluid was conducted to emphasize the role of viscosity in negative wavefront velocity. By the comparison of the dambreak front locations from analytical, experimental, and numerical data, the effects of viscosity on the dambreak flow have been examined. In line with this, the influence of ambient water depth on the front propagation’s average velocity has been investigated. Finally, the air bubble characteristics, such as area, shape, and lifetime under the effects of fluid viscosity and surface tension, have been explored.
The capture mechanism of fibrous filters in a wet condition is studied by focusing on the single droplet impact to an initial droplet attached to the fiber. Highspeed photography and numerical simulation are conducted to study the collision phenomenon. The eccentricity between the mass center of the impacting droplet and the initial droplet is varied to evaluate the threshold capture velocity of the impacting droplet. The eccentricity is considered to be composed of two perpendicular components. The distance between the impacting droplet trajectory line and fiber axis is considered as one of the components of eccentricity ( \(e_{1}\) ). The distance between the mass center of the impacting droplet and the initial droplet along the fiber axis is defined as the other component of eccentricity ( \(e_{2}\) ). The initial droplet volume is also varied in our investigation. It is observed that increasing the initial droplet volume attached to the fiber as well as increasing the eccentricity \(e_{1}\) reduces the threshold capture velocity of the impacting droplet. However, increasing \(e_{2}\) increases the threshold capture velocity. Surprisingly, for an impacting droplet with a radius of R colliding with a small volume initial droplet of a radius of \(R_{i}\) at \(e_{2}> 0.85\) ( \(R+R_{i}\) ), the threshold capture velocity is found to be higher than that of a droplet impacting on a dry fiber.
Highfrequency ventilation is a type of mechanical ventilation therapy applied on patients with damaged or delicate lungs. However, the transport of oxygen down, and carbon dioxide up, the airway is governed by subtle transport processes which hitherto have been difficult to quantify. We investigate one of these mechanisms in detail, nonlinear mean streaming, and the impact of the onset of turbulence on this streaming, via direct numerical simulations of a model 1:2 bifurcating pipe. This geometry is investigated as a minimal unit of the fractal structure of the airway. We first quantify the amount of gas recirculated via mean streaming by measuring the recirculating flux in both the upper and lower branches of the bifurcation. For conditions modeling the tracheatobronchi bifurcation of an infant, we find the recirculating flux is of the order of 3–5% of the peak flux . We also show that for conditions modeling the upper generations, the mean recirculation regions extend a significant distance away from the bifurcation, certainly far enough to recirculate gas between generations. We show that this mean streaming flow is driven by the formation of longitudinal vortices in the flow leaving the bifurcation. Second, we show that conditional turbulence arises in the upper generations of the airway. This turbulence appears only in the flow leaving the bifurcation, and at a point in the cycle centered around the maximum instantaneous flow rate. We hypothesize that its appearance is due to an instability of the longitudinalvortices structure.
We propose a simple model for the evolution of an inviscid vortex sheet in a potential flow in a channel with parallel walls. This model is obtained by augmenting the Birkhoff–Rott equation with a potential field representing the effect of the solid boundaries. Analysis of the stability of equilibria corresponding to flat sheets demonstrates that in this new model the growth rates of the unstable modes remain unchanged as compared to the case with no confinement. Thus, in the presence of solid boundaries the equilibrium solution of the Birkhoff–Rott equation retains its extreme form of instability with the growth rates of the unstable modes increasing in proportion to their wavenumbers. This linear stability analysis is complemented with numerical computations performed for the nonlinear problem which show that confinement tends to accelerate the growth of instabilities in the nonlinear regime.
Parametrically excited standing waves are observed on a cylindrical fluid filament. This is the cylindrical analog of the Faraday instability in a flat surface or spherical droplet. Using Floquet theory, a linear stability analysis is carried out on a viscous cylindrical fluid surface, which is subjected to a timeperiodic radial acceleration. Viscosity of the fluid has a significant impact on the critical forcing amplitude as well as the dispersion relation of the nonaxisymmetric patterns. The effect of viscosity on the threshold of the pattern with azimuthal wavenumber \(m=1\) shows a different dependence from \(m>1\) . It is also observed that the effect of viscosity is greater on the threshold with higher m.
Large scale industrial combustion devices, for example, internal combustion engines, gas turbine combustors, etc., operate under highpressure conditions and utilize a variety of fuels. Unfortunately, the majority of the current numerical combustion modelling approaches are not fully validated for highpressure and the nonunity Lewis number ( \(\hbox {Le} =\) thermal diffusivity/mass diffusivity) effects in premixed turbulent combustion. In any case, a numerical model needs to be checked for the effects of these parameters to guarantee generality of the model. In the present study, these two critical features of the models are numerically explored utilizing fundamental elements of several algebraic flame surface density reaction rate closure models accessible in the open literature. The Lewis number impact is likewise examined utilizing LES of recently published subgrid scale fractal flame surface density model, which indicated acceptable results for high and lowpressure methane fuelled applications. The computed numerical results are compared with an extensive experimental dataset for lean methane and propane fuels featuring various flow and turbulence conditions at operating pressures in the range of 1–10 bar. The quantitative results from most of the selected models do not show the experimentally observed trends at highpressures and for nonunity Le number fuels. Modifications to the models are incorporated to reflect effects of these two important parameters utilizing a broad parametric investigation resulting in a satisfactory agreement with the experimental data.
The mass transport in electrokinetically actuated microchannel flow is interesting when the wall reactions influence the wall potential, thereby affecting the hydrodynamics. This is the first work where the electroosmotic flow is impacted by the chemical reactions. Since the wall potential is nonuniform, we have compared the results of the classical Poisson–Boltzmann equations with the generalized Poisson–Nernst–Planck model and investigated the applicability within the range of the operating conditions of the problem. The results provide fundamental understanding of the velocity profile within the channel and the wall concentration, which is significantly different from the classical species transport. The wall concentration is dependent on the electrokinetic parameters rather than the Reynolds and Peclet number solely. For constant volumetric flow rate, the resultant electroosmotic velocity profile is not parabolic and exhibits higher convection close to the wall, leading to reduced solute polarization. The overall mass transport rate can be enhanced by more than two times with respect to nonelectrical phenomena. The results will be useful in understanding the physics and provide operational knowhow of electrokineticbased applications related to capillary electrophoresis, electrochromatrogaphy and (bio)chemical sensing.
The physical characteristics and evolution of a largescale helium plume are examined through a series of numerical simulations with increasing physical resolution using adaptive mesh refinement (AMR). The five simulations each model a 1mdiameter circular helium plume exiting into a \((4~\hbox {m})^3\) domain and differ solely with respect to the smallest scales resolved using the AMR, spanning resolutions from 15.6 mm down to 0.976 mm. As the physical resolution becomes finer, the helium–air shear layer and subsequent Kelvin–Helmholtz instability are better resolved, leading to a shift in the observed plume structure and dynamics. In particular, a critical resolution is found between 3.91 and 1.95 mm, below which the mean statistics and frequency content of the plume are altered by the development of a Rayleigh–Taylor (RT) instability near the centerline in close proximity to the plume base. Comparisons are made with prior experimental and computational results, revealing that the presence of the RT instability leads to reduced centerline axial velocities and higher puffing frequencies than when the instability is absent. An analysis of velocity and scalar gradient quantities, and the dynamics of the vorticity in particular, show that gravitational torque associated with the RT instability is responsible for substantial vorticity production in the flow. The gridconverged simulations performed here indicate that very high spatial resolutions are required to accurately capture the nearfield structure and dynamics of largescale plumes, particularly with respect to the development of fundamental flow instabilities.
The equations governing the dynamics of a periodically driven microspheroid in an unsteady viscous fluid at low Reynolds number are derived. Its oscillation properties in the presence/absence of memory forces are reported. The core part of the derivation is a perturbation analysis of motion of a sphere. The calculated solutions match with those available in the literature in the limiting case of a sphere. The dependence of the solutions on shape ( \(\alpha \) ), free oscillation frequency ( \(\omega _0\) ) and particle–fluid density ratio ( \(d_r\) ) is calculated. The maximum amplitude of the oscillations of an oblate spheroid is greater than that of a prolate spheroid, showing that the velocity disturbance for an oblate spheroid is higher in the presence/absence of the memory force. The increase in \(\alpha \) leads to the enhancement(reduction) of amplitude peaks in the case of the oblate (prolate) spheroid in the presence and more dominantly in the absence of the force. There is also a reduction in the amplitude of spheroid oscillations of many multiples due to the presence of the memory force. Stronger oscillation variations are observed on changing \(\omega _0\) or \(d_r\) compared to \(\alpha .\) The variations of the value of the phase are similar for both the spheroids on varying \(\omega _0\) and \(d_r\) , whereas they are reversed on varying \(\alpha .\) The linear scaling of amplitude on \(\alpha \) observed for the spheroids may give insight into the physics, especially regarding the quantum of velocity disturbances due to particle size. The slopes are high in the absence of the force, confirming that the presence of the force increases the resistance of spheroid motion, largely. The dependencies of oscillations on the parameters can be utilized for better separation of particles or for characterizing the suspension. The novelty of the problem and its analytical solutions might have value as tests in software for more complicated and realistic systems and hence strikes a good balance between complication and tractability.
In this paper, the influence of the Mach number on the stability of twodimensional compressible planar wakes is studied to gain physical insight into the turbine wakes. Twodimensional instabilities of compressible wakes are studied using local spatiotemporal instability analyses. The absolute/convective boundary of a family of wake profiles is obtained at different Mach numbers. Then, local stability analyses of compressible wakes behind flat plates are performed. It is found that in the subsonic region increasing Mach number acts in two ways to modify the instability characteristics in the near wake region: it lengthens the recirculation zone and it reduces the absolute growth rate. These two mechanisms work against each other, which explains why the linear global growth rate varies slightly as Mach number changes in the subsonic region. Further increasing Mach number to 1 would greatly reduce the length of the absolute unstable region due to the occurrence of expansion waves around the trailing edge corner. As a result, the wake is strongly stabilized at \(\hbox {Ma}=1\) .