Development of a higher-order accurate kinetic wave/particle flux-splitting algorithm for the Euler equations

The development of a novel second-order accurate both in time and space kinetic scheme, called the Kinetic Wave/Particle Split (KWPS) scheme is reported in this paper. It is demonstrated that the first-order KWPS algorithm, while computationally efficient and robust, is very diffusive on a reasonable mesh. The KWPS scheme is derived by employing the following steps: the molecular velocity in the Boltzmann equation is split as a sum of fluid velocity and thermal (peculiar) velocity, thus the flux vector in the Boltzmann equation is divided into a convective part and an acoustic part. The Boltzmann equation is then discretized using an upwind differencing. Moments of the discretized Boltzmann equation with the collision invariant vector and Maxwellian distribution function then yield the KWPS scheme for the Euler equations. The second-order formulation is obtained through the application of a Taylor series expansion of the Maxwellian distribution function to include the first-order derivatives. Numerical test cases, both in 1-D and 2-D, are computed to demonstrate the improved accuracy of the second-order KWPS scheme, while maintaining both the efficiency and robustness of the first-order scheme. It should be noted that the new second-order KWPS formulation cannot be obtained using the standard numerical approach employed in the literature for second-order extension. The methodology employed in this paper can be easily extended to formulate a KWPS scheme to any order of accuracy. [Copyright &y& Elsevier]