Multidimensional On-lattice Higher-order Models in the Thermal Lattice Boltzmann Theory

摘要

We present a set of uniform polynomial equations that providesmultidimensional on-lattice higher-order models of the lattice Boltzmanntheory, while keeping compact the number of discrete velocities. As examples,we explicitly derive two- and three-dimensional on-lattice models applicable todescribing thermal compressible flows of the accuracy levels of theNavier-Stokes equations with smaller numbers of discrete velocities incomparison to the existing models. We demonstrate the accuracy and stability ofthe three-dimensional model by using the Riemann problem.