| Summary: | 博士 === 國立臺灣大學 === 應用力學研究所 === 90 === The relativistic kinetic flux vector splitting (KFVS) method is derived based on the special theory of relativity, the relativistic Boltzmann equation and the equilibrium, i.e., the Jüttner-Maxwell distribution function. The numerical first-order and the MUSCL-type second order schemes with van Leer limiters are developed in local rest frame and their counterparts in other inertial moving frames are obtained by Lorentz transformation, whose general transformation matrix is given in Appendix A and is formulated according to the one-dimensional Lorentz transformation in associated with the three-dimensional coordinate rotations. Both schemes are validated by the problems of one-dimensional Sod’s shock tube with different initial conditions and are applied to the two-dimensional spherical explosive waves.
The intrinsic flaw of the original KFVS method is investigated. Due to the splitting of integration intervals for the distribution function, the propagation velocities of the macroscopic physical quantities are discrepant, which results in the breakdown of the conservation relations. The modified intervals of integration and the conditions for the KFVS method satisfying the conservation relations are proposed both for the classical and relativistic gas dynamics.
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