A simplified conservation flux scheme for gas kinetics based on OpenFOAM framework I: Shakhov model

A solver for the Shakhov model equation, founded on dugksFOAM, has been successfully developed. This was achieved through the application of a conservation-type gas kinetic scheme with a simplified interface flux. The process begins with the updating of macroscopic quantities. Subsequently, the distribution function is computed using these newly updated values. This innovative approach effectively mitigates errors that might occur during the integration of the distribution function, especially when an unstructured velocity space is employed. The solver offers two distinct methods for velocity space integration. The first is a traditional structured space, which can be conveniently adjusted and configured via input files. The second is an unstructured space, which utilizes fewer discrete velocity points. These points are determined based on the mesh files provided by the user. In this unstructured approach, the velocity points are strategically positioned to strike an optimal balance between computing efficiency and precision, thereby enhancing the overall performance and accuracy of the solver. The solver's hybrid parallelization technique, specifically the X-space parallelization approach that encompasses both physical and velocity spaces, empowers the efficient execution of large-scale three-dimensional simulations. By subjecting the solver to benchmark cases such as shock tube problems, lid-driven cavity flow, Poiseuille flow, and flows past cylinders, sphere and X-38 vehicle, the accuracy and dependability of this solver have been thoroughly validated and verified. This comprehensive verification process not only benchmark cases the solver's robustness in handling diverse fluid dynamics scenarios but also highlights its potential for broader applications in the field of computational fluid dynamics.