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In this paper, we present a unified gas-kinetic wave-particle (UGKWP) methodon unstructured mesh for multiscale simulation of continuum and rarefied flow.Inheriting from the multicale transport in the unified gas-kinetic scheme(UGKS), the integral solution of kinetic model equation is employed in theconstruction of UGKWP method to model the flow physics in the cell size andtime step scales. A novel wave-particle adaptive formulation is introduced inthe UGKWP method to describe the flow dynamics in each control volume. Thelocal gas evolution is constructed through the dynamical interaction of thedeterministic hydrodynamic wave and the stochastic kinetic particle. Within theresolution of cell size and time step, the decomposition, interaction, andevolution of the hydrodynamic wave and the kinetic particle depend on the ratioof the time step to the local particle collision time. In the rarefied flowregime, the flow physics is mainly recovered by the discrete particles and theUGKWP method performs as a stochastic particle method. In the continuum flowregime, the flow behavior is solely followed by macroscopic variable evolutionand the UGKWP method becomes a gas-kinetic hydrodynamic flow solver for theviscous and heat-conducting Navier--Stokes solutions. In different flowregimes, many numerical test cases are computed to validate the UGKWP method onunstructured mesh. The UGKWP method can get the same UGKS solutions in allKnudsen regimes without the requirement of the time step and mesh size beingless than than the particle collision time and mean free path. With anautomatic wave-particle decomposition, the UGKWP method becomes very efficient.For example, at Mach number 30 and Knudsen number 0.1, in comparison with UGKSseveral-order-of-magnitude reductions in computational cost and memoryrequirement have been achieved by UGKWP.

Unified Gas-kinetic Wave-Particle Methods II: Multiscale Simulation on Unstructured Mesh