Taylor-Green Vortex Research Articles

A High Accuracy Preserving Parallel Algorithm for Compact Schemes for DNS

A new accuracy-preserving parallel algorithm employing compact schemes is presented for direct numerical simulation of the Navier-Stokes equations. Here the connotation of accuracy preservation is having the same level of accuracy obtained by the proposed parallel compact scheme, as the sequential code with the same compact scheme. Additional loss of accuracy in parallel compact schemes arises due to necessary boundary closures at sub-domain boundaries. An attempt to circumvent this has been done in the past by the use of Schwarz domain decomposition and compact filters in “A new compact scheme for parallel computing using domain decomposition,” J. Comput. Phys. 220, 2 (2007), 654--677, where a large number of overlap points was necessary to reduce error. A parallel compact scheme with staggered grids has been used to report direct numerical simulation of transition and turbulence by the Schwarz domain decomposition method. In the present research, we propose a new parallel algorithm with two benefits. First, the number of overlap points is reduced to a single common boundary point between any two neighboring sub-domains, thereby saving the number of points used, with resultant speed-up. Second, with a proper design, errors arising due to sub-domain boundary closure schemes are reduced to a user designed error tolerance, bringing the new parallel scheme on par with sequential computing. Error reduction is achieved by using global spectral analysis, introduced in “Analysis of central and upwind compact schemes,” J. Comput. Phys. 192, 2, (2003) 677--694, which analyzes any discrete computing method in the full domain integrally. The design of the parallel compact scheme is explained, followed by a demonstration of the accuracy of the method by solving benchmark flows: (1) periodic two-dimensional Taylor-Green vortex problem; (2) flow inside two-dimensional square lid-driven cavity (LDC) at high Reynolds number; and (3) flow inside a non-periodic three-dimensional cubic LDC with the staggered grid arrangement.

High-order kinetic flow solver based on the flux reconstruction framework.

The goal of this paper is to develop a high-order numerical method based on the kinetic inviscid flux (KIF) method and flux reconstruction (FR) framework. The KIF aims to find a balance between the excellent merits of the gas-kinetic scheme (GKS) and the lower computational costs. The idea of KIF can be viewed as an inviscid-viscous splitting version of the gas-kinetic scheme, and Shu and Ohwada have made the fundamental contribution. The combination of totally thermalized transport (TTT) scheme and kinetic flux vector splitting (KFVS) method are achieved in KIF. Using a coefficient which is related to time step and averaged collision time, KIF can adjust the weights of TTT and KFVS flux in the simulation adaptively. By doing the inviscid-viscous splitting, KIF is very suitable and easy to integrate into the existing framework. The well-understood FR framework is used widely for the advantages of robustness, economical costs, and compactness. The combination of KIF and FR is originated by three motivations. The first purpose is to develop a high-order method based on the gas-kinetic theory. The second reason is to keep the advantages of GKS. The last aim is that the designed method should be more efficient. In present work, we use the KIF method to replace the Riemann flux solver applied in the interfaces of elements. The common solution at the interface is computed according to the gas-kinetic theory, which makes the combination of KIF and FR scheme more reasonable and available. The accuracy and performance of present method are validated by several numerical cases. The Taylor-Green vortex problem has been used to verify its potential to simulate turbulent flows.

On the Behaviour of High-Order One-Step Monotonicity-Preserving Scheme for Direct Numerical Simulation of Shocked Turbulent Flows

The objective of this paper is to check the ability of the high-order OSMP scheme [Daru, V., and C. Tenaud. 2004. “HighOrder One-Step Monotonicity-Preserving Schemes for Unsteady Compressible Flow Calculations.” Journal of Computational Physics 193 (2): 563–594] to accurately compute turbulent compressible flows with a special focus on the effect of the MP constraints on solutions of wall bounded turbulent shocked flows. We first validate numerical approaches on two canonical test cases: the 3D Taylor-Green vortex and the steady 2D shock-wave laminar boundary layer interaction. The emblematic case where a shock wave interacts with a turbulent boundary layer is then simulated. We conclude that the OSMP scheme coupled with a centred 2nd-order approximation for the diffusive fluxes constitutes a reliable numerical tool for the DNS of compressible turbulent shocked flows, that is completely competitive compared to other approaches since the overall errors are lowered of about one order of magnitude for the same grid resolution.

Application of Gene Expression Programming to a-posteriori LES modeling of a Taylor Green Vortex

Gene Expression Programming (GEP), a branch of machine learning, is based on the idea to iteratively improve a population of candidate solutions using an evolutionary process built on the survival-of-the-fittest concept. The GEP approach was initially applied with encouraging results to the modeling of the unclosed tensors in the context of RANS (Reynolds Averaged Navier–Stokes) turbulence modeling. In a subsequent study it was demonstrated that the GEP concept can also be successfully used for modeling the unknown Sub-Grid Stress (SGS) tensor in the context of Large Eddy Simulations (LES). This was done in an a-priori analysis, where an existing Direct Numerical Simulation (DNS) database was explicitly filtered to evaluate the unknown stresses and to assess the performance of model candidates suggested by GEP. This paper presents the next logical step, i.e. the application of GEP to a-posteriori LES model development. Because a-posteriori analysis, using in-the-loop optimization, is considered the ultimate way to test SGS models, this can be considered an important milestone for the application of machine learning to LES based turbulence modeling. GEP is here used to train LES models for simulating a Taylor Green Vortex (TGV) and results are compared with existing standard models. It is shown that GEP finds a model that outperforms known models from literature as well as the no-model LES. Although the performance of this best model is maintained for resolutions and Reynolds numbers different from the training data, this is not automatically guaranteed for all other models suggested by the algorithm.

An improved dealiasing scheme for the fourth‐order Runge‐Kutta method: Formulation, accuracy and efficiency analysis

SummaryIn 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.

Inline vector compression for computational physics

A novel inline data compression method is presented for single-precision vectors in three dimensions. The primary application of the method is for accelerating computational physics calculations where the throughput is bound by memory bandwidth. The scheme employs spherical polar coordinates, angle quantisation, and a bespoke floating-point representation of the magnitude to achieve a fixed compression ratio of 1.5. The anisotropy of this method is considered, along with companding and fractional splitting techniques to improve the efficiency of the representation. We evaluate the scheme numerically within the context of high-order computational fluid dynamics. For both the isentropic convecting vortex and the Taylor–Green vortex test cases, the results are found to be comparable to those without compression. Performance is evaluated for a vector addition kernel on an NVIDIA Titan V GPU; it is demonstrated that a speedup of 1.5 can be achieved.

High-order upwind compact finite-difference lattice Boltzmann method for viscous incompressible flows

In this work, a high-order upwind compact finite-difference lattice Boltzmann method (UCDLBM) is developed to efficiently solve viscous incompressible flow problems. A fifth-order upwind compact difference scheme is adopted to discretize the spatial derivatives of the lattice Boltzmann equation, and the third-order total-variation-diminishing Runge–Kutta scheme is utilized for the discretization of the temporal term. Compared to the existing central compact finite-difference lattice Boltzmann method (CFDLBM), the present UCDLBM can prevent non-physical oscillations without filtering due to the natural dissipative property of upwind schemes. Three benchmark problems involving the Taylor–Green vortex problem, the doubly periodic shear layer flow problem and the lid driven square cavity flow problem are numerically solved to demonstrate the accuracy and efficiency of the present method. Numerical results computed are in good agreement with the analytical solution or other available numerical results. And, the present UCDLBM is less time-consuming than the CFDLBM without degenerating the order of accuracy of the numerical solutions.

A unified framework of continuous and discontinuous Galerkin methods for solving the incompressible Navier–Stokes equation

In this paper, we propose a unified numerical framework for the time-dependent incompressible Navier–Stokes equation which yields the H1-, H(div)-conforming, and discontinuous Galerkin methods with the use of different viscous stress tensors and penalty terms for pressure robustness. Under minimum assumption on Galerkin spaces, the semi- and fully-discrete stability is proved when a family of implicit Runge–Kutta methods are used for time discretization. Furthermore, we present a unified discussion on the penalty term. Numerical experiments are presented to compare our schemes with classical schemes in the literature in both unsteady and steady situations. It turns out that our scheme is competitive when applied to well-known benchmark problems such as Taylor–Green vortex, Kovasznay flow, potential flow, lid driven cavity flow, and the flow around a cylinder.

Efficient two-step Runge-Kutta methods for fluid dynamics simulations

Explicit two-step Runge-Kutta (TSRK) methods offer an efficient alternative to traditional explicit Low-Storage Runge-Kutta (LSRK) schemes for solving the Navier-Stokes equations. A special class of TSRK methods that reduce requirement compared to previous TSRK schemes are derived. Schemes of fourth, fifth and sixth order are implemented and tested.The new schemes are evaluated with two common test cases, a 2D cylinder and a 3D Taylor-Green vortex. The results are compared with classical time discretization strategies. Timings obtained in three different hardware configurations show that the new TSRK methods of order four are 25% faster than LSRK schemes of the same order.Fifth and sixth order TSRK methods are tested with the same 3D test case and the results are compared to LSRK algorithms. Results show TSRK schemes of fifth and sixth order are competitive compared to LSRK methods of the same orders, as LSRK methods are of second order for non linear differential systems.

Assessing Stretched-Vortex Subgrid-Scale Models in Finite Volume Methods for Unbounded Turbulent Flows

Simulations of complex, compressible, high-Reynolds-number flows require high-fidelity physics and turbulence models to be appropriately coupled with strong numerical regularization methods. Obtaining grid-independent and scheme-independent solutions of these flows when using both explicit turbulence models and additional numerical regularization is especially important for further testing and development of accurate physics models. To this end, the current study investigates the interaction between the stretched-vortex subgrid-scale model and both the fourth-order piecewise parabolic limiter and a fifth-order upwinding interpolation (or hyperviscosity). It is demonstrated that computing the subgrid-scale kinetic energy estimate for the stretched-vortex model at a coarser resolution than the base mesh provides results which are independent of the use of numerical regularization techniques. This is shown to be the case for a temporally-evolving shear-layer, the inviscid Taylor–Green vortex problem, and a decaying, homogeneous turbulent flow.

Comparison of the convergence rates between Fourier pseudo-spectral and finite volume method using Taylor-Green vortex problem

Numerical methods are one of the ways to solve problems represented by differential equations; these methods are implemented through algorithms and must be submitted to a numerical verification process to obtain reliable values. The verification of two numerical methods is presented in this study: the Fourier pseudo-spectral method (FPSM) and the finite-volume method (FVM), with and without the immersed boundary method (IBM). Both methodologies are used for incompressible two-dimensional flows, where the use of the IBM allows the modeling of flows involving complex geometries. The present study evaluates the accuracy and convergence rate of the FPSM and FVM using the Taylor-Green decaying vortex problem. The results show that, with the use of the IBM, FPSM and FVM reach the fourth and second order of numerical convergence, respectively, with a longer processing time in simulations with the FPSM.

Split form ALE discontinuous Galerkin methods with applications to under-resolved turbulent low-Mach number flows

The construction of discontinuous Galerkin (DG) methods for the compressible Euler or Navier-Stokes equations (NSE) includes the approximation of non-linear flux terms in the volume integrals. The terms can lead to aliasing and stability issues in turbulence simulations with moderate Mach numbers (Ma≲0.3), e.g. due to under-resolution of vortical dominated structures typical in large eddy simulations (LES). The kinetic energy or entropy is elevated in smooth, but under-resolved parts of the solution which are affected by aliasing. It is known that the kinetic energy is not a conserved quantity for compressible flows, but for small Mach numbers minor deviations from a conserved evolution can be expected. While it is formally possible to construct kinetic energy preserving (KEP) and entropy conserving (EC) DG methods for the Euler equations, due to the viscous terms in case of the NSE, we aim to construct kinetic energy dissipative (KED) or entropy stable (ES) DG methods on moving curved hexahedral meshes. The Arbitrary Lagrangian-Eulerian (ALE) approach is used to include the effect of mesh motion in the split form DG methods. First, we use the three dimensional Taylor-Green vortex to investigate and analyze our theoretical findings and the behavior of the novel split form ALE DG schemes for a turbulent vortical dominated flow. Second, we apply the framework to a complex aerodynamics application. An implicit LES split form ALE DG approach is used to simulate the transitional flow around a plunging SD7003 airfoil at Reynolds number Re=40,000 and Mach number Ma=0.1. We compare the standard nodal ALE DG scheme, the ALE DG variant with consistent overintegration of the non-linear terms and the novel KED and ES split form ALE DG methods in terms of robustness, accuracy and computational efficiency.

A forward-backward probabilistic algorithm for the incompressible Navier-Stokes equations

A novel probabilistic scheme for solving the incompressible Navier-Stokes equations is studied, in which we approximate a generalized nonlinear Feyman-Kac formula. The velocity field is interpreted as the mean value of a stochastic process ruled by Forward-Backward Stochastic Differential Equations (FBSDEs) driven by Brownian motion. Following an approach by Delbaen, Qiu and Tang introduced in 2015, the pressure term is obtained from the velocity by solving a Poisson problem as computing the expectation of an integral functional associated to an extra BSDE. The FBSDEs components are numerically solved by using a forward-backward algorithm based on Euler type schemes for the local time integration and the quantization of the increments of Brownian motion following the algorithm proposed by Delarue and Menozzi in 2006. Numerical results are reported on spatially periodic analytic solutions of the Navier-Stokes equations for incompressible fluids. We illustrate the proposed algorithm on a two dimensional Taylor-Green vortex and three dimensional Beltrami flows.

Low-Mach hybrid lattice Boltzmann-finite difference solver for combustion in complex flows

A hybrid solver for low-Mach combustion simulations has been proposed and validated through different test-cases in a previous publication [Hosseini et al., “Hybrid lattice Boltzmann-finite difference model for low Mach number combustion simulation,” Combust. Flame 209, 394–404 (2019)]. However, all the considered configurations were laminar, far from realistic applications. To check the performance of this approach for more complex physical processes, the developed solver is used here to model a variety of transitional and turbulent reacting flows. It is first used to compute an established benchmark, the Taylor–Green vortex, for (a) an iso-thermal single-component fluid, (b) a thermal non-reacting mixture, and (c) a thermal reacting mixture (hydrogen/air flame). Detailed comparisons of the results against a high-order in-house direct numerical simulation solver show that the proposed hybrid lattice Boltzmann solver correctly captures the dynamics of the flow at relatively low numerical cost. This same solver is then used to model the interaction of a methane/air flame with a vortex pair, revealing different interaction regimes of interest for turbulent combustion models. It is further employed to model the interaction of an expanding circular flame kernel with a pair of vortices and correctly captures the characteristic regimes. To showcase its ability to deal with turbulent flows, it is finally applied to a homogeneous isotropic turbulent configuration.

Entropy-stable p-nonconforming discretizations with the summation-by-parts property for the compressible Navier–Stokes equations

The entropy-conservative/stable, curvilinear, nonconforming, p-refinement algorithm for hyperbolic conservation laws of Del Rey Fernández et al. (2019) is extended from the compressible Euler equations to the compressible Navier–Stokes equations. A simple and flexible coupling procedure with planar interpolation operators between adjoining nonconforming elements is used. Curvilinear volume metric terms are numerically approximated via a minimization procedure and satisfy the discrete geometric conservation law conditions. Distinct curvilinear surface metrics are used on the adjoining interfaces to construct the interface coupling terms, thereby localizing the discrete geometric conservation law constraints to each individual element. The resulting scheme is entropy conservative/stable, element-wise conservative, and freestream preserving. Viscous interface dissipation operators that retain the entropy stability of the base scheme are developed. The accuracy and stability of the resulting numerical scheme are shown to be comparable to those of the original conforming scheme in Carpenter et al. (2014) and Parsani et al. (2016), i.e., this scheme achieves ∼p+1/2 convergence on geometrically high-order distorted element grids; this is demonstrated in the context of the viscous shock problem, the Taylor–Green vortex problem at a Reynolds number of Re=1,600, and a subsonic turbulent flow past a sphere at Re=2,000.

Assessment of SGS Models for Large Eddy Simulation (LES) of a Stratified Taylor–Green Vortex

Eddy viscosity-based and regularization-based subgrid-scale (SGS) models are quantitatively assessed for large eddy simulations (LES) of stratified Taylor–Green vortex (TGV). LES calculations using the dynamic Smagorinsky, Leray- $$\alpha$$ , LANS- $$\alpha$$ and Clark- $$\alpha$$ models are conducted using a pseudo-spectral formulation on a $$128^{3}$$ grid and using $$\alpha =\frac{1}{160}$$ (for all the regularization models) for Froude number, $$Fr_0=\frac{{\mathcal {U}}}{{{\mathcal {N}}}{{\mathcal {L}}}}=1$$ , and Reynolds number, $$Re_{0}= \frac{\mathcal {U L} }{\nu }=1600$$ . Results are compared in detail with in-house direct numerical simulation (DNS) calculations. Validation of the formulation is carried out through grid-dependent studies using grids of $$64^3$$ , $$128^3$$ and $$256^3$$ , $$\alpha$$ (regularization parameter)-dependent studies using $$\alpha$$ values of $$\frac{1}{40}, \frac{1}{80}, \frac{1}{160}$$ and $$\frac{1}{320}$$ , and comparisons with previously published results Remmler and Hickel, 2012, of the same problem. Various quantities including turbulent kinetic energy (tke), turbulent potential energy (tpe), Q-criteria based vortical structures, potential & total energy spectra, and horizontal & vertical energy fluxes in the respective directions, are analyzed to understand the capability of the various LES models in predicting the development of stratified turbulence. Results showed that all the SGS model predictions were very similar to each other with Smagorinsky and Leray displaying the lowest and highest errors, respectively, in comparison to DNS. The effect of $$Fr_0$$ was also studied through additional LES calculations at $$Fr_0=0.5$$ and 0.16, again using the dynamic Smagorinsky and regularization models and comparing various parameters including tke, tpe and energy spectra to DNS. Decay rates of tke and tpe decreased and turbulence was significantly suppressed with decrease in $$Fr_0$$ . At these lower $$Fr_0$$ , all the SGS model predictions were almost identical to each other and compared extremely well with the DNS results.

Evaluation of a nonlinear variational multiscale method for fluid transport problems

Diverse transport problems, especially those based on fluid flow models, are intrinsically multiscale and nonlinear, characteristics that often lead to intricate dynamics such as the development of instabilities and turbulence. Computational simulations that resolve all scales in these problems are often unfeasible, prompting to coarse-grained simulation strategies in which small-scale features are modeled instead of resolved. Variational Multiscale (VMS) methods, and particularly residual-based Large-Eddy Simulation (LES) approaches, have proven effective and robust for the coarse-grained simulation of complex transport problems. VMS methods avoid the assumption of separable nonlinearity and the reliance on empirical small-scale models by using a variational decomposition of scales together with a residual-based approximation of the small-scales. Evaluation of a nonlinear VMS approach, denoted as VMSn, is presented for the coarse-grained simulation of transient-advective-diffusive-reactive (TADR) transport problems arising from fluid flow models. In contrast to classical VMS approaches that neglect the effect of the small scales on the transport operator, VMSn treats the inter-dependence between large- and small-scales upfront. The treatment of inter-scale coupling involves the solution of a local algebraic nonlinear system describing the evolution of the small-scales. The VMSn approach is complemented with two algebraic approximations of the small-scales: one based on the main diagonal of the transport matrices and another that preserves transport fluxes and is suitable for generic TADR systems. The suitability of the VMSn approach for handling general TADR problems and regimes is evaluated with benchmark incompressible, compressible, and magnetohydrodynamic laminar flow problems, the incompressible Taylor-Green vortex flow, the turbulent free jet, and the two-temperature arc in crossflow. Simulation results show that VMSn leads to minor improvements in accuracy with respect to the classical VMS for the laminar flow problems, but to significantly greater accuracy for the turbulent flows and the unsteady plasma flow problems, while using the same cohesive numerical formulation.

Non-linear instability analysis of the three-dimensional Navier–Stokes equations: Taylor–Green vortex problem

The three-dimensional (3D) Taylor–Green vortex (TGV) flow is one of the simplest systems to study the generation of different scales of vortices due to the growth of disturbances via effects of different physical mechanisms, including vortex-stretching as an additional source for instability, showing not only the creation of turbulence but also turbulent decay. The strong anisotropic and well-organized flow becomes unstable at early time due to transfer of energy to small scales. The analysis of instability of the periodic 3D TGV flow for the Reynolds number of Re = 2000 is reported here. The direct numerical simulation of the periodic 3D TGV flow is carried out using high accuracy numerical methods for the (vector-potential, vorticity)-formulation, which exactly satisfy the solenoidality condition for vector-potential and vorticity in the computational domain. The evolution of disturbances is examined using the instability theories of the disturbance mechanical energy of the Navier–Stokes equation and the role of rotationality by the disturbance enstrophy transport equation (DETE), which is derived from the enstrophy transport equation. The 3D TGV flow exhibits a tornado-type structure at the center of the domain at intermediate stages of transition to turbulence, which is analyzed using the vortex-identification method of λ2-criteria and the DETE method, as described by Sengupta et al. [“Tracking disturbances in transitional and turbulent flows: Coherent structures,” Phys. Fluids 31(12), 124106 (2019)]. Here, it is observed that the coherent structure is diffused in the λ2-contours. Third generation vortex-identification methods are analyzed for capturing the transient, rotating vortex. The combination of new Omega- and the Liutex/Rortex-methods, as reviewed by C. Liu et al. [“Third generation of vortex identification methods: Omega and Liutex/Rortex based systems,” J. Hydrodyn. 31(2), 205–223 (2019)], captures the evolution of the transient vortex, but the structure identified by these methods appears to be diffused, while the DETE method clearly captures the vortex geometry and highlights the formation of the vortex at early times to aid in predicting the flow evolution.

Direct numerical simulation of supersonic flow and acoustics over a compression ramp

We present direct numerical simulations of the shock wave boundary layer interaction (SBLI) at Mach number 2.9 over a 24° ramp. We study both the numerical accuracy and flow physics. Two classes of spatial reconstruction schemes are employed: the monotonic upstream-centered scheme for conservation laws and the Weighted Essentially Non-Oscillatory (WENO) scheme, of accuracy ranging from 2nd- to 11th-order. Using the canonical Taylor–Green vortex test-case, a simple and computationally inexpensive rescaling of the candidate stencil values—within the context of the high-order WENO scheme—is proposed for reducing the numerical dissipation, particularly in under-resolved simulations. For the compression ramp case, higher-order schemes are shown to capture the size of the SBLI separation zone more accurately, a consequence of resolving much finer turbulence structures. For second- and fifth-order schemes, the energy of the unresolved small scale turbulence shifts the cascade of the turbulence kinetic energy (TKE) spectrum, thus resulting in more energetic large scale turbulent structures. Consequently, the λ-shock foot shifts further downstream, leading to a smaller separation bubble size. Nonetheless, other statistical quantities, such as the turbulence anisotropy invariant map and the turbulence kinetic energy budget terms, show little dependence on the type and order of the spatial reconstruction scheme. Finally, using the more accurate ninth-order WENO results, it is reasoned that the interaction of the λ-shock with the post-shock relaxation region drives the low-frequency oscillation of the λ-shock.

Semi-Lagrangian lattice Boltzmann method for compressible flows.

This work thoroughly investigates a semi-Lagrangian lattice Boltzmann (SLLBM) solver for compressible flows. In contrast to other LBM for compressible flows, the vertices are organized in cells, and interpolation polynomials up to fourth order are used to attain the off-vertex distribution function values. Differing from the recently introduced Particles on Demand (PoD) method [Dorschner, Bösch, and Karlin, Phys. Rev. Lett. 121, 130602 (2018)PRLTAO0031-900710.1103/PhysRevLett.121.130602], the method operates in a static, nonmoving reference frame. Yet the SLLBM in the present formulation grants supersonic flows and exhibits a high degree of Galilean invariance. The SLLBM solver allows for an independent time step size due to the integration along characteristics and for the use of unusual velocity sets, like the D2Q25, which is constructed by the roots of the fifth-order Hermite polynomial. The properties of the present model are shown in diverse example simulations of a two-dimensional Taylor-Green vortex, a Sod shock tube, a two-dimensional Riemann problem, and a shock-vortex interaction. It is shown that the cell-based interpolation and the use of Gauss-Lobatto-Chebyshev support points allow for spatially high-order solutions and minimize the mass loss caused by the interpolation. Transformed grids in the shock-vortex interaction show the general applicability to nonuniform grids.