scholarly journals Numerical Modeling of Self-Consistent Dynamics of Shallow and Ground Waters

2021 ◽  
pp. 45-62
Author(s):  
Sergey Khrapov
Keyword(s):  
Numerical Modeling ◽  
Numerical Solution ◽  
Software Package ◽  
Simulation Software ◽  
Second Order ◽  
Order Of Accuracy ◽  
Ground Waters ◽  
Spatially Inhomogeneous ◽  
Tvd Method ◽  
Joint Dynamics

A mathematical and numerical model of the joint dynamics of shallow and ground waters has been built, which takes into account the nonlinear dynamics of a liquid, water absorption from the surface into the ground, filtration currents in the ground, and water seepage from the ground back to the surface. The dynamics of shallow waters is described by the Saint-Venant equations, taking into account the spatially inhomogeneous distributions of the terrain, the coefficients of bottom friction and infiltration, as well as non-stationary sources and flows of water. For the numerical integration of Saint-Venant’s equations, the well-tested CSPH-TVD method of the second order of accuracy is used, the parallel CUDA algorithm of which is implemented as a software package “EcoGIS-Simulation” for high-performance computing on supercomputers with graphic coprocessors (GPU). The dynamics of groundwater is described by the nonlinear Bussensk equation, generalized to the case of a spatially inhomogeneous distribution of the parameters of the porous medium and the surface of the aquiclude (the boundary between water-permeable and low-permeable soils). The numerical solution of this equation is built on the basis of a finite-difference scheme of the second order of accuracy, the CUDA algorithm of which is integrated into the calculation module of the “EcoGIS-Simulation” software package and is consistent with the main stages of the CSPH-TVD method. The relative deviation of the numerical solution from the exact solution of the nonlinear Boussinesq equation does not exceed 10−4–10−5. The paper compares the results of numerical modeling of the dynamics of groundwater with analytical solutions of the linearized Bussensk equation used as calculation formulas in the methods for predicting the level of groundwater in the vicinity of water bodies. It is shown that the error of these methods is several percent even for the simplest case of a plane-parallel flow of groundwater with a constant backwater. Based on the results obtained, it was concluded that the proposed method for numerical modeling of the joint dynamics of surface and ground waters can be more versatile and efficient (it has significantly better accuracy and productivity) in comparison with the existing methods for calculating flooding zones, especially for hydrodynamic flows with complex geometry and nonlinear interaction of counter fluid flows arising during seasonal floods during flooding of vast land areas.

Numerical solution of a source identification problem: Almost coercivity

2019 ◽  
Vol 27 (4) ◽  
pp. 457-468 ◽  
Author(s):  
Allaberen Ashyralyev ◽  
Abdullah Said Erdogan ◽  
Ali Ugur Sazaklioglu
Keyword(s):  
Numerical Solution ◽  
Source Identification ◽  
Identification Problem ◽  
Second Order ◽  
Numerical Results ◽  
Difference Schemes ◽  
Stability Estimates ◽  
Order Of Accuracy ◽  
Accuracy Difference ◽  
Coercive Stability

Abstract The present paper is devoted to the investigation of a source identification problem that describes the flow in capillaries in the case when an unknown pressure acts on the system. First and second order of accuracy difference schemes are presented for the numerical solution of this problem. Almost coercive stability estimates for these difference schemes are established. Additionally, some numerical results are provided by testing the proposed methods on an example.

scholarly journals Study on Accuracy of the High-Resolution Schemes

2014 ◽  
Vol 6 ◽  
pp. 905053
Author(s):  
Yawen Tang ◽  
Bo Yu ◽  
Jianyu Xie ◽  
Jingfa Li ◽  
Peng Wang
Keyword(s):  
High Resolution ◽  
Numerical Solution ◽  
Richardson Extrapolation ◽  
Second Order ◽  
Order Accuracy ◽  
Order Of Accuracy ◽  
Numerical Examples ◽  
High Resolution Schemes ◽  
Artificial Diffusion ◽  
Convection Dominated

The high-resolution (HR) schemes have been widely used as they can achieve the numerical solution without oscillation and artificial diffusion, especially for convection-dominated problems. However, there still have arguments about the order of accuracy of HR schemes, especially about the extreme value of the solution. In this paper, it is proved that any HR scheme designed in the NVD diagram has second-order accuracy when its combined segments totally locate in the BAIR region. In other words, it has been verified in our study that the segments, which have low-order accuracy when independently employed, have at least second-order accuracy when locate in BAIR region by analysis of two implementation methods of HR scheme and also a number of numerical examples. Meanwhile Richardson extrapolation has been used to estimate the order of accuracy of HR schemes which achieve the same conclusion.

scholarly journals A Rotary Compression Process for Producing Hollow Gear Shafts

Materials ◽  
2020 ◽  
Vol 13 (24) ◽  
pp. 5718
Author(s):  
Arkadiusz Tofil ◽  
Janusz Tomczak ◽  
Tomasz Bulzak ◽  
Zbigniew Pater ◽  
Marcin Buczaj ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Numerical Modeling ◽  
Material Flow ◽  
Software Package ◽  
Experimental Tests ◽  
Simulation Software ◽  
The Finite Element Method ◽  
Compression Process ◽  
Manufacturing Method ◽  
Stepped Shaft

This paper presents selected numerical and experimental results of a study investigating the process of forming hollow stepped gear shafts from tubes by rotary compression. The objective of the study was to determine whether the rotary compression process is an effective method of producing hollow stepped gear shafts and to identify limitations of this manufacturing method. A theoretical analysis involved the numerical modeling of the proposed process by the finite element method (FEM). 3D simulations were performed using the commercial simulation software package Simufact Forming. The analysis involved examining the material flow pattern along with thermal and force parameters of the process. The FEM results were verified with experimental tests conducted under laboratory conditions. The experiments were performed on a machine specially designed for the rotary compression of hollow parts. Results demonstrate that it is difficult to form a stepped gear shaft in one operation. For this reason, such parts should be formed in two operations. The first operation involves the forming of a hollow stepped shaft by rotary compression, while in the second operation, a gear is formed on one of the steps of the shaft.

On the construction of orthogonal curvilinear grids for regional oceanic modeling: algorithm and user guide

2020 ◽  
Vol 48 (4) ◽  
pp. 45-111
Author(s):  
A. F. Shepetkin
Keyword(s):  
Inverse Problem ◽  
Numerical Solution ◽  
Elliptic Problem ◽  
Software Package ◽  
Conformal Transformation ◽  
Iterative Procedure ◽  
Geometric Shape ◽  
Curvilinear Grids ◽  
Grid Points ◽  
Grid Nodes

A new algorithm for constructing orthogonal curvilinear grids on a sphere for a fairly general geometric shape of the modeling region is implemented as a “compile-once - use forever” software package. It is based on the numerical solution of the inverse problem by an iterative procedure -- finding such distribution of grid points along its perimeter, so that the conformal transformation of the perimeter into a rectangle turns this distribution into uniform one. The iterative procedure itself turns out to be multilevel - i.e. an iterative loop built around another, internal iterative procedure. Thereafter, knowing this distribution, the grid nodes inside the region are obtained solving an elliptic problem. It is shown that it was possible to obtain the exact orthogonality of the perimeter at the corners of the grid, to achieve very small, previously unattainable level of orthogonality errors, as well as make it isotropic -- local distances between grid nodes about both directions are equal to each other.

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