A positivity-preserving scheme for fluctuating hydrodynamics

A finite-difference hybrid numerical method for the solution of isothermal fluctuating hydrodynamic equations is proposed. The primary focus to ensure positivity-preserving property scheme, which critical its functionality and reliability especially when simulating vapour systems. Both cases single- two-phase flows are considered by exploiting van der Waals' square-gradient approximation model fluid (often referred as “diffuse-interface” model). accuracy robustness proposed scheme verified against several benchmark theoretical predictions statistical properties density, velocity fluctuations liquid-vapour interface, including static structure factor density field spectrum capillary waves excited thermal at interface. Finally, applied challenging bubble nucleation process, shown capture salient features phenomenon, namely rate subsequent bubble-growth dynamics.