title: Multidimensional on-lattice higher-order models in the thermal lattice Boltzmann theory.
abstract: We present a set of uniform polynomial equations that provides multidimensional on-lattice higher-order models of the lattice Boltzmann theory while keeping compact the number of discrete velocities. As examples, we explicitly derive one-, two-, and three-dimensional on-lattice models applicable to describing thermal compressible flows of the accuracy levels of the Navier-Stokes equations with smaller numbers of discrete velocities in comparison to the existing models. We demonstrate the accuracy and stability of the one-, two-, and three-dimensional models by using the Riemann problem.
authors: KIST and University of Science and Technology, 136-791, Seoul, Korea.
authors: Jae Wan
authors: JW
authors: Shim