Simulation of Vertical Movements of Seawater in Stratified Reservoirs

Abstract

Introduction. In the field of computational mathematics, there are many ways to approximate the model of fluid mechanics. Methods and estimates of approximation quality criteria, such as stability and convergence, are developed, while a combination of approaches to constructing economical difference schemes, such as splitting by physical processes, regularization by B. N. Chetverushkin, a linear combination of the Upwind and Standard Leapfrog difference schemes in aggregate has not been implemented and evaluated before. The authors were faced with the task of approximating each part of the hydrodynamic model split by physical processes with the most adequate scheme and further investigating the correctness of this approach.Materials and Methods. The mathematical model of hydrophysical processes is closed by the empirical equation of the state of salt water. Significant properties were selected, a mathematical model was built. Difference operators approximated differential operators. An algorithm for layer-by-layer modeling of transients was constructed. The algorithm has been implemented in the form of the program, which mainly contains elementwise (massively-parallel) operations.Results. Mathematical models of hydrodynamic processes in reservoirs were obtained, taking into account three equations of motion in the presence of a density gradient of the aqueous medium when hydrostatic approximation was abandoned. A new method of calculating the pressure field using B. N. Chetverushkin’s regularizers in the continuity equation was tested. A software module for numerical simulation of hydrophysical processes of water movement with different salinity and density was developed. This is open-source software that provides not only the redefinition of empirical dependences (as algebraic functions), but also the connection of external simulating modules to display dependences algorithmically.Discussion and Conclusion. The developed model of hydrophysics, taking into account the properties of salt water and the dynamic relationship of the mechanical movement of water with salinity, can be used to study the formation of a nonequilibrium distribution of parameters and identify the most stable parameters of the aquatic environment. The model explains the downward movement of oxygen. That will help in the future to estimate the values of the parameters of the aquatic environment, which are difficult to measure directly. It can be used in the procedure of parametric identification of hard-to-measure parameters of the aquatic environment.

Keywords

• mathematical model
• stratification
• seawater dynamics model
• quasi-hydrodynamic model
• cell occupancy method
• central difference scheme
• sweep method
• ftcs scheme
• upwind leapfrog
• standard leapfrog