## 1 Introduction
It handles discontinuities in the fluid by solving the Riemann problem. It has the most negligible numerical viscosity in monotone flux, but the computational complexity is too large. The Lax-Friedrichs (LF) flux solver [15] ensures stability by adding a large amount of numerical viscosity. Although it is sufficiently stable, it introduces large numerical dissipation when solving discontinuities, resulting in low resolution of the calculation results. In contrast, the ROE flux solver [16] achieves more accurate discontinuity capture by linearizing the nonlinear system and handling the linear Riemann problem. The HLL solver proposed by [PERSON] [17] introduces a simpler approximate Riemann solver that does not need to solve the complete characteristic structure. Instead, it calculates the flux through a double-wave approximation. However, it has poor resolution for contact discontinuities. In order to improve accuracy further, the HLLC [16; 17] solver adds an intermediate contact wave based on HLL to capture the details in complex flows better. [PERSON] [18; 19] proposed the AUSM solver, which achieved efficient and accurate flux calculation by separating convection and pressure effects. Two years later, the AUMS+ [20] scheme was proposed, which overcame some limitations of the original AUSM method by improving the flux splitting method, enhancing low-speed stability, and improving shock wave capture accuracy. The HLEM [21] solver improves the HLL method and enhances the ability to capture vortices and contact discontinuities. Besides the aforementioned Riemann solver, the lattice Boltzmann method (LBM) [22; 23; 24], proposed in recent years, is being utilized as a selective computational fluid dynamics method and is widely used in various fields. However, when LBM is applied globally to address the control equations across the entire flow field, several issues arise, including limitations on uniform grid size and its relationship to the time step. To address these problems, an innovative approach called the lattice Boltzmann flux solver (LBFS) [25; 26; 27] was proposed, which is mainly applied at the cell interface, thus overcoming the aforementioned limitations of LBM. Lattice Boltzmann models have been widely used and verified for compressible and incompressible problems, multiphase flow, and other problems [28; 29; 30; 31; 32; 33; 34]. The one-dimensional lattice Boltzmann model proposed by [PERSON] et al. [35; 36], as well as [PERSON] et al. [37; 38], successfully simulates compressible flow problems with strong shock waves. However, when these models are applied to work out high-speed flow problems, the results may oscillate, become unstable and diverge, or even become unphysical solutions. To address these problems, [PERSON] et al. [39] proposed the D1Q4 model with no free parameters, which performs well in high-speed Mach number flow situations, where D1 indicates that the model is a one-dimensional lattice Boltzmann model and Q4 indicates that the model contains four lattice velocities. [PERSON] [9] proposed a finite difference-based WENO scheme, which uses the Lax-Friedrichs flux splitting technique to separate the numerical flux into positive and negative parts, directly reconstructs the numerical flux using the WENO scheme, and adds dissipation to improve stability. The LBFS scheme based on molecular kinetic theory has good approximation performance for the Riemann solution and has been successfully coupled with the Monotonic Upstream-centered Scheme for Conservation Laws (MUSCL) scheme and the Piecewise Parabolic Method with Directional Elements (PPMDE) scheme [40]. [PERSON] [41] developed a rotating lattice Boltzmann flux solver (RLBFS) based on LBFS and the finite volume method by decomposing the external normal of the cell interface into two mutually perpendicular vectors, making the calculation results more stable. It may be noted that the RLBFS was initially developed using the finite volume method and had only the second order of accuracy.