Adaptive criterion and modification of wave-particle decomposition in UGKWP method for high-speed flow simulation

Benefiting from its direct modeling of physical laws in discretized space and its automatic decomposition of hydrodynamic waves and particles, the unified gas-kinetic wave-particle (UGKWP) method provides significant advantages for a wide range of multiscale physical problems, including hypersonic flow, plasma transport, and radiation transport. To achieve a more effective and efficient wave-particle decomposition in high-speed flow simulations, particularly in regions with drastic scale variations, this work investigates a scale-adaptive criterion and introduces modifications to the flux evolution of the UGKWP method. In addition to the intrinsic time-based criterion embedded in the time-dependent distribution function of UGKWP, two further criteria-based on spatial resolution and local gradients–are employed to identify the local scale and reduce the computational overhead of particles in representing near-equilibrium gas distributions. Furthermore, by aligning the evolution of hydrodynamic waves with the coefficients in the time–integration flux of the unified gas-kinetic scheme (UGKS), the modified wave representation improves consistency with particle contributions, which is especially critical when flow scales vary significantly across computational cells. The effectiveness of the adaptive UGKWP method is demonstrated through a series of benchmark cases, including hypersonic flows around a cylinder at various inflow Knudsen numbers, hypersonic flow over a slender cavity, side-jet impingement in hypersonic flow, and three-dimensional hypersonic flows over a 70^∘ blunted cone with a cylindrical sting.