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The Particles on Demand method [B. Dorschner, F. B\"{o}sch and I. V. Karlin,{\it Phys. Rev. Lett.} {\bf 121}, 130602 (2018)] was recently formulated with aconservative finite volume discretization and validated against challengingbenchmarks. In this work, we rigorously analyze the properties of the referenceframe transformation and its implications on the accuracy of the model. Basedon these considerations, we propose strategies to boost the efficiency of thescheme and to reduce the computational cost. Additionally, we generalize themodel such that it includes a tunable Prandlt number via quasi-equilibriumrelaxation. Finally, we adapt concepts from the multi-scale semi-Lagrangianlattice Boltzmann formulation to the proposed framework, further improving thepotential and the operating range of the kinetic model. Numerical simulationsof high Mach compressible flows demonstrate excellent accuracy and stability ofthe model over a wide range of conditions.

Particles on Demand method: theoretical analysis, simplification techniques and model extensions