Academician Xiong is also the chief professor of research group of stellar structure, evolution and pulsation. His research area is stellar convection theory and related aspects of stellar structure, evolution and oscillation. Academician Xiong's main academic contribution is the establishment of a new statistical theory of non-local convection to replace the traditional mixing-length theory. His theory is based on hydrodynamic equations and turbulence theory, and therefore it can depict stellar convection more precisely.
- He developed a statistical theory of time-dependent convection independently, and then generalized it to treat nonradial stellar oscillations, which is now the only feasible convection theory to treat nonradial stellar oscillations.
- Using the time-dependent convection theory, he calculated the oscillations of variable stars and explained the existence of the red edge of instability strip successfully, which has been the most important unresolved problem of pulsations of variable stars since 1970s.
- He developed a statistical theory of non-local convection independently, and then generalized it to treat stellar evolution with chemicaly inhomogeneous stars. It is now the only non-local convection theory that can deal with chemical ununiformity.
- Using the non-local convection theory, he calculated the evolution of massive stars and solved the well-known semi-convection contradiction. The new evolutionary tracks run at a higher luminosity, and the main sequence band is wider than those indicated by traditional theories. This is favorable to resolving the contradiction between the observational and theoretical distribution of the luminous stars in the H-R diagram. It may also solve the well-known Cepheid mass discrepancy problem.
- Using the non-local convection theory, he calculated the structure of the solar convection zone. The temperature distribution, the turbulent velocity and the turbulent temperature fields agreed well with the observation. His theory also predicts that going through the boundary of the convectively unstable zone, the turbulent velocity-temperature correlation changes its sign, while the mixing-length theory contradicts the observation. Moreover, the new theory gives accordant bottom boundary of the convection zone with that given by helioseismology, which may be used to explain the Lithium and Beryllium depletions.
K.G.Petrovay once said it was the best model of solar convection zone.