scholarly journals Local quasigeoid modelling in Slovakia using the finite volume method on the discretized Earth's topography

2020 ◽  
Vol 50 (3) ◽  
pp. 287-302
Author(s):  
Róbert ČUNDERLÍK ◽  
Matej MEDĽA ◽  
Karol MIKULA
Keyword(s):  
Numerical Solution ◽  
Finite Volume Method ◽  
Finite Volume ◽  
Large Scale ◽  
Horizontal Resolution ◽  
Geopotential Model ◽  
Computational Domain ◽  
Disturbing Potential ◽  
Volume Method ◽  
Upper Boundary

The paper presents local quasigeoid modelling in Slovakia using the finite volume method (FVM). FVM is used to solve numerically the fixed gravimetric boundary value problem (FGBVP) on a 3D unstructured mesh created above the real Earth's surface. Terrestrial gravimetric measurements as input data represent the oblique derivative boundary conditions on the Earth's topography. To handle such oblique derivative problem, its tangential components are considered as surface advection terms regularized by a surface diffusion. The FVM numerical solution is fixed to the GOCE-based satellite-only geopotential model on the upper boundary at the altitude of 230 km. The horizontal resolution of the 3D computational domain is 0.002 × 0.002 deg and its discretization in the radial direction is changing with altitude. The created unstructured 3D mesh of finite volumes consists of 454,577,577 unknowns. The FVM numerical solution of FGBVP on such a detailed mesh leads to large-scale parallel computations requiring 245 GB of internal memory. It results in the disturbing potential obtained in the whole 3D computational domain. Its values on the discretized Earth's surface are transformed into the local quasigeoid model that is tested at 404 GNSS/levelling benchmarks. The standard deviation of residuals is 2.8 cm and decreases to 2.6 cm after removing 9 identified outliers. It indicates high accuracy of the obtained FVM-based local quasigeoid model in Slovakia.

High-resolution numerical modelling of the altimetry-derived gravity disturbances and disturbing gradients

2020 ◽  
Author(s):  
Róbert Čunderlík ◽  
Marek Macák ◽  
Michal Kollár ◽  
Karol Mikula
Keyword(s):  
High Resolution ◽  
Numerical Solution ◽  
Finite Volume ◽  
Sea Surface ◽  
Computational Domain ◽  
Disturbing Potential ◽  
Gravity Disturbances ◽  
Mean Sea Surface ◽  
Upper Boundary ◽  
Goce Satellite

<p>Recent high-resolution mean sea surface models obtained from satellite altimetry in a combination with the GRACE/GOCE-based global geopotential models provide valuable information for detailed modelling of the altimetry-derived gravity data. Our approach is based on a numerical solution of the altimetry-gravimetry boundary-value problem using the finite volume method (FVM). FVM discretizes the 3D computational domain between an ellipsoidal approximation of the Earth's surface and an upper boundary chosen at a mean altitude of the GOCE satellite orbits. A parallel implementation of the finite volume numerical scheme and large-scale parallel computations on clusters with distributed memory allow to get a high-resolution numerical solution in the whole 3D computational domain. Our numerical experiment presents the altimetry-derived gravity disturbances and disturbing gradients determined with the high-resolution 1 x 1 arc min at two altitude levels; on the reference ellipsoid and at the altitude of 10 km above the ellipsoid. As input data, the Dirichlet boundary conditions over oceans/seas are considered in the form of the disturbing potential. It is obtained from the geopotential evaluated on the DTU18 mean sea surface model from the GO_CONS_GCF_2_TIM_R5 geopotential model and then filtered using the nonlinear diffusion filtering. On the upper boundary, the FVM solution is fixed to the disturbing potential generated from the GO_CONS_GCF_2_DIR_R5 model while exploiting information from the GRACE and GOCE satellite missions.</p>

Numerical Solution of Multidimensional Compressible Flow by High Order Nodal Discontinuous Galerkin Method

2013 ◽  
Vol 392 ◽  
pp. 100-104 ◽  
Author(s):  
Fareed Ahmed ◽  
Faheem Ahmed ◽  
Yong Yang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Solution ◽  
Finite Volume Method ◽  
Discontinuous Galerkin ◽  
Finite Volume ◽  
High Order ◽  
Numerical Predictions ◽  
Volume Method ◽  
Element Method

In this paper we present a robust, high order method for numerical solution of multidimensional compressible inviscid flow equations. Our scheme is based on Nodal Discontinuous Galerkin Finite Element Method (NDG-FEM). This method utilizes the favorable features of Finite Volume Method (FVM) and Finite Element Method (FEM). In this method, space discretization is carried out by finite element discontinuous approximations. The resulting semi discrete differential equations were solved using explicit Runge-Kutta (ERK) method. In order to compute fluxes at element interfaces, we have used Roe Approximate scheme. In this article, we demonstrate the use of exponential filter to remove Gibbs oscillations near the shock waves. Numerical predictions for two dimensional compressible fluid flows are presented here. The solution was obtained with overall order of accuracy of 3. The numerical results obtained are compared with experimental and finite volume method results.

An Explicit Modeling Approach for Simulating Fluid-Structure Interaction Problems With Immersed-Boundary Finite-Volume Method

2019 ◽  
Author(s):  
Yanbo Huang ◽  
Shanshan Li ◽  
Zhenhai Pan
Keyword(s):  
Finite Volume Method ◽  
Finite Volume ◽  
Numerical Experiments ◽  
Fluid Structure Interaction ◽  
Immersed Boundary ◽  
Computational Domain ◽  
Fluid Structure ◽  
Structure Interaction ◽  
Modeling Approach ◽  
Volume Method

Abstract Fluid-structure interaction (FSI) is an important fundamental problem with wide scientific and engineering applications. The immersed boundary method has proved to be an effective way to model the interaction between a moving solid and its surrounding fluid. In this study, a novel modeling approach based on the coupled immersed-boundary and finite-volume method is proposed to simulate fluid-structure interaction problems. With this approach, the whole computational domain is treated as fluid and discretized by only one set of Eulerian grids. The computational domain is divided into solid parts and fluid parts. A goal velocity is locally determined in each cell inside the solid part. At the same time, the hydrodynamic force exerted on the solid structure is calculated by integrating along the faces between the solid cells and fluid cells. In this way, the interaction between the solid and fluid is solved explicitly and the costly information transfer between Lagranian grids and Eulerian grids is avoided. The interface is sharply restricted into one single grid width throughout the iterations. The proposed modeling approach is validated by conducting several classic numerical experiments, including flow past static and freely rotatable square cylinders, and sedimentation of an ellipsoid in finite space. Throughout the three numerical experiments, satisfying agreements with literatures have been obtained, which demonstrate that the proposed modeling approach is accurate and robust for simulating FSI problems.

Calculation of the Unsteady Gas Flow Around a Projectile Moving Through a Gun Barrel

2003 ◽  
Author(s):  
Valery Ponyavin ◽  
Roald Akberov ◽  
Yitung Chen ◽  
Hsuan-Tsung Hsieh ◽  
Darrell W. Pepper
Keyword(s):  
Shock Waves ◽  
Flow Pattern ◽  
Finite Volume Method ◽  
Finite Volume ◽  
Gas Flow ◽  
Computational Domain ◽  
Gun Barrel ◽  
Volume Method ◽  
Unsteady Gas Flow ◽  
Velocity Pressure

The calculation of gas flow during the motion of a projectile in the gun barrel is a complicated computational task due of the presence of numerous factors, such as nonisothermicity, turbulence, changes in the shape of the computational domain with time, etc. In this study, an attempt to calculate the characteristics of gas flow around a projectile during the motion of the projectile in the gun barrel is undertaken. The flow is considered axisymmetrical, nonstationary, nonisothermal, compressible, and turbulent. For calculating the flow around the projectile, the finite volume method was employed. During the motion of the projectile, the flow pattern behind it changed from subsonic to supersonic. The results of the calculations are represented in figures depicting the flow at different moments of time. The figures show the fields of velocity, pressure and density, as well as the appearance of shock waves inside the gun barrel at subsonic and supersonic speeds.

scholarly journals Three-Dimensional Hydrostatic Curved Channel Flow Simulations Using Non-Staggered Triangular Grids

Water ◽  
2022 ◽  
Vol 14 (2) ◽  
pp. 174
Author(s):  
Wei Zhang ◽  
Miguel Uh Uh Zapata ◽  
Damien Pham Van Pham Van Bang ◽  
Kim Dan Nguyen
Keyword(s):  
Finite Volume Method ◽  
Finite Volume ◽  
Channel Flow ◽  
Large Scale ◽  
Three Dimensional ◽  
Ocean Modeling ◽  
Curved Channel ◽  
Triangular Grids ◽  
Vortex Pattern ◽  
Volume Method

Non-staggered triangular grids have many advantages in performing river or ocean modeling with the finite-volume method. However, horizontal divergence errors may occur, especially in large-scale hydrostatic calculations with centrifugal acceleration. This paper proposes an unstructured finite-volume method with a filtered scheme to mitigate the divergence noise and avoid further influencing the velocities and water elevation. In hydrostatic pressure calculations, we apply the proposed method to three-dimensional curved channel flows. Approximations reduce the numerical errors after filtering the horizontal divergence operator, and the approximation is second-order accurate. Numerical results for the channel flow accurately calculate the velocity profile and surface elevation at different Froude numbers. Moreover, secondary flow features such as the vortex pattern and its movement along the channel sections are also well captured.

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