Yongle Liu

Bio: Yongle Liu is an academic researcher from Southern University of Science and Technology. The author has contributed to research in topics: Shallow water equations & Computer science. The author has an hindex of 4, co-authored 8 publications receiving 33 citations. Previous affiliations of Yongle Liu include Harbin Institute of Technology.

Moist-convective thermal rotating shallow water model

Abstract: We show how the moist-convective rotating shallow water model, where the moist convection and the related latent heat release are incorporated into the standard rotating shallow water model of the atmosphere, can be improved by introducing, in a self-consistent way, horizontal gradients of potential temperature and changes of the latter due to the condensation heating, radiative cooling, and ocean-atmosphere heat fluxes. We also construct the quasi-geostrophic limit of the model in mid-latitudes and its weak-gradient limits in the equatorial region. The capabilities of the new model are illustrated by the examples of convection-coupled gravity waves and equatorial waves produced by the relaxation of localized pressure and potential temperature anomalies in the presence of moist convection.

Thermal versus isothermal rotating shallow water equations: comparison of dynamical processes by simulations with a novel well-balanced central-upwind scheme

Abstract: We introduce a new high-resolution well-balanced central-upwind scheme for two-dimensional rotating shallow water equations with horizontal temperature/density gradients – thermal rotating shallow

Numerical dissipation switch for two-dimensional central-upwind schemes

Abstract: We propose a numerical dissipation switch, which helps to control the amount of numerical dissipation present in central-upwind schemes. Our main goal is to reduce the numerical dissipation without risking oscillations. This goal is achieved with the help of a more accurate estimate of the local propagation speeds in the parts of the computational domain, which are near contact discontinuities and shears. To this end, we introduce a switch parameter, which depends on the distributions of energy in the x - and y -directions. The resulting new central-upwind is tested on a number of numerical examples, which demonstrate the superiority of the proposed method over the original central-upwind scheme.

Well-Balancing via Flux Globalization: Applications to Shallow Water Equations with Wet/Dry Fronts

Abstract: We study the flux globalization based central-upwind scheme from Cheng et al. (J Sci Comput 80:538–554, 2019) for the Saint-Venant system of shallow water equations. We first show that while the scheme is capable of preserving moving-water equilibria, it fails to preserve much simpler “lake-at-rest” steady states. We then modify the computation of the global flux variable and develop a well-balanced scheme, which can accurately handle both still- and moving-water equilibria. In addition, we extend the flux globalization based central-upwind scheme to the case when “dry” and/or “almost dry” areas are present. To this end, we introduce a hybrid approach: we use the flux globalization based scheme inside the “wet” areas only, while elsewhere we apply the central-upwind scheme from Bollermann et al. (J Sci Comput 56:267–290, 2013), which is designed to accurately capture wet/dry fronts. We illustrate the performance of the proposed schemes on a number of numerical examples.

Geophysical fluid dynamics: understanding (almost) everything with rotating shallow water models

Abstract: Fluid dynamics is a broad field within fluid mechanics that deals with the flow of fluids such as liquids and gases under various conditions, mostly with the dynamics of flows on macroscopic scales...

Moist-convective thermal rotating shallow water model

Abstract: We show how the moist-convective rotating shallow water model, where the moist convection and the related latent heat release are incorporated into the standard rotating shallow water model of the atmosphere, can be improved by introducing, in a self-consistent way, horizontal gradients of potential temperature and changes of the latter due to the condensation heating, radiative cooling, and ocean-atmosphere heat fluxes. We also construct the quasi-geostrophic limit of the model in mid-latitudes and its weak-gradient limits in the equatorial region. The capabilities of the new model are illustrated by the examples of convection-coupled gravity waves and equatorial waves produced by the relaxation of localized pressure and potential temperature anomalies in the presence of moist convection.

Thermal versus isothermal rotating shallow water equations: comparison of dynamical processes by simulations with a novel well-balanced central-upwind scheme

Abstract: We introduce a new high-resolution well-balanced central-upwind scheme for two-dimensional rotating shallow water equations with horizontal temperature/density gradients – thermal rotating shallow