Dimension-Reduced Hyperbolic Moment Method for the Boltzmann Equation with BGK-Type Collision (Communications in Computational Physics, 2014)
We develop the dimension-reduced hyperbolic moment method for theBoltzmann equation, to improve solution efficiency using a numerical regularizedmoment method for problems with low-dimensional macroscopic variables and high-dimensional microscopic variables. In the present work, we deduce the globally hyperbolic moment equations for the dimension-reduced Boltzmann equation based on theHermite expansion and a globally hyperbolic regularization. The numbers of Maxwellboundary condition required for well-posedness are studied. The numerical schemeis then developed and an improved projection algorithm between two different Hermite expansion spaces is developed. By solving several benchmark problems, we validate the method developed and demonstrate the significant efficiency improvementby dimension-reduction.