The Exploration And Research Of Hydrodynamics For River Bend On The Curvilinear Coordinates

The simulated flow is generally described by the Saint-Venant equations or Navier-Stokes equations. Governing equations which contain continuum equation, momentum equation and energy equation are derived from mass, momentum and energy conservation after the molecular collision. By coordinate transformation, the govening equations can be transformed into curvilinear coordinates, which can calculate for natural rivers more exactly. This paper gets governing equations from BGK Boltzmann equation by integral, and all of this are done on the orthogonal curvilinear coordinates system.BGK Boltzamann equation can be used for establishing hydrodynamic model, one of the advantages of this method is that it meets the entropy condition. Based on the coherence between Boltzmann equation and the macro-conservation laws, we could solve the macro-variable differential equation model by the Boltzmann equation. But now, most of BGK Boltzmann methods are used in the Cartesian coordinate system. For describeing the complex irregular geometric boundary of the rivers, reducing errors and instability, BGK Boltzmann method will be transfered to curvilinear coordinates, because the shape of the natural rivers are bend, it is difficult to simulated complicated bend rivers on the Cartesian coordinate system. This paper mainly do research in the following aspects:1. Choose the orthogonal curvilinear coordinates along the centerline of the river, get the BGK Boltzmann equation from coordinate transformation.2. Base on the basic relationships between macro-variables and micro-variables, get the two-dimensional governing equations by taking the moment of the BGK Boltzmann equation on the orthogonal curvilinear coordinates, prove the consistency of the Boltzmann equation and the macro-conservation laws.3. Establish a numerical model and get numerical simulation based on the curve flume experiments. The results show that the model have good simulation capability for the meandering flow.The results of this paper laid the foundation for the research of the microcosmic method in hydrodynamics by using the Boltzmann equation on the orthogonal curvilinear coordinates, have the theoretical and the practical application significance.