Research On Numerical Scheme And Computing Method For Non-hydrostatic Ocean Model

Ocean model is an important tool for marine science and Earth System science research.Due to the limited computing power,the hydrostatic approximation was commonly used in the early ocean models to filter out fast fluctuations and reduce the computational complexity.However,the hydrostatic approximation,with the improvement of the model resolution,is becoming less valid.With the rapid development of supercomputer technology and the increasing interest of scientists for small-scale internal waves,convection and symmetric instability,the non-hydrostatic ocean model has become an important trend of model development.Even though there are a few ocean models capable of non-hydrostatic simulation,the non-hydrostatic ocean models still face many problems in terms of computational stability and efficiency.First,the accurate simulation for the non-hydrostatic ocean motions is inseparable from the long-term stability of the non-hydrostatic ocean model.Ensuring the computational stability of the model has always been one of the difficulties in the development of the dynamic framework of the model.For spatial discretization,this thesis derived a generalized antisymmetric operator expression for the primitive equations through variable transformation,and designed a discrete generalized antisymmetric space operator which is compatible with the continuous space operator through the transformation of some equation terms.For temporal discretization,a semi-implicit numerical scheme was designed based on the operator splitting model with second-order accuracy.The quadratic conservation of the system is completely maintained through an adjustable parameter,so as to ensure the long-term computational stability of the model.Second,the calculation of the non-hydrostatic pressure is the main bottleneck of the non-hydrostatic ocean model,which becomes more troublesome in the coordinate system.The calculation of non-hydrostatic pressure is generally transformed into solving a three-dimensional Poisson equation,the non-orthogonality of the coordinate system brings higher computational complexity to this process.In this thesis,a new semi-implicit and variable layer algorithm was proposed for the non-hydrostatic pressure calculation.This new algorithm rules out the effect caused by the non-orthogonality of the coordinate system,which allows it to simplify the coefficient matrix of the discrete Poisson equation,such as eliminating extra non-zero elements and getting rid of asymmetric shape.Furthermore,this new algorithm was applied in large-scale parallel test.In the test,the overall computational efficiency of the model was improved by about 30%.Finally,a new non-hydrostatic ocean model was designed and constructed based on the general efficient auto-parallel computing framework developed by our research group.This new model has the potential of universality,it can comply with the increasingly complex supercomputer hardware structure and satisfy the demand for a sustainable development.Besides,this model has a concise software structure.In the strong and weak scaling tests with a parallelism of 3840 cores,this model achieves a parallel efficiency level of82.8% and 82.0%,respectively.With the upgrading and optimization of our auto-parallel computing framework,this model is expected to be efficiently transplanted between different computing platforms in the future.