Erratum to: Analysis of critical ricochet angle using two space discretization methods

To analyze the transient response of transformer windings under very fast transient over-voltage (VFTO), multi-conductor transmission line (MTL) model based on the representation of transformer windings by its individual turns are established. Space discretization is needed for solving the time-domain telegraph equations of MTL. To calculate the voltage distributions along transformer windings, through combining the compact finite difference (CFD) theory and the backward differentiation formulas (BDF). Simulation software ATP is introduced, and the simulation results demonstrate that the proposed approach is feasible.

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Calculation of the Quasi Three-Dimensional Flow in a Turbomachine Blade Row

Journal of Engineering for Power ◽

10.1115/1.3446252 ◽

1977 ◽

Vol 99 (1) ◽

pp. 53-62 ◽

Cited By ~ 1

Author(s):

Jean-Pierre Veuillot

Keyword(s):

Finite Difference ◽

Three Dimensional ◽

Three Dimensional Flow ◽

Through Flow ◽

Blade Row ◽

Time Marching ◽

Space Discretization ◽

Finite Volume Approach ◽

Marching Method ◽

Finite Difference Techniques

The equations of the through flow are obtained by an asymptotic theory valid when the blade pitch is small. An iterative method determines the meridian stream function, the circulation, and the density. The various equations are discretized in an orthogonal mesh and solved by classical finite difference techniques. The calculation of the steady transonic blade-to-blade flow is achieved by a time marching method using the MacCormack scheme. The space discretization is obtained either by a finite difference approach or by a finite volume approach. Numerical applications are presented.

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A New Global Spatial Discretization Method for Calculating Dynamic Responses of Two-Dimensional Continuous Systems With Application to a Rectangular Kirchhoff Plate

Journal of Vibration and Acoustics ◽

10.1115/1.4037176 ◽

2017 ◽

Vol 140 (1) ◽

Cited By ~ 2

Author(s):

K. Wu ◽

W. D. Zhu

Keyword(s):

Boundary Conditions ◽

Continuous System ◽

Dynamic Responses ◽

Kirchhoff Plate ◽

Continuous Systems ◽

Discretization Method ◽

Two Dimensional ◽

Spatial Discretization ◽

Arbitrary Boundary ◽

Discretization Methods

A new global spatial discretization method (NGSDM) is developed to accurately calculate natural frequencies and dynamic responses of two-dimensional (2D) continuous systems such as membranes and Kirchhoff plates. The transverse displacement of a 2D continuous system is separated into a 2D internal term and a 2D boundary-induced term; the latter is interpolated from one-dimensional (1D) boundary functions that are further divided into 1D internal terms and 1D boundary-induced terms. The 2D and 1D internal terms are chosen to satisfy prescribed boundary conditions, and the 2D and 1D boundary-induced terms use additional degrees-of-freedom (DOFs) at boundaries to ensure satisfaction of all the boundary conditions. A general formulation of the method that can achieve uniform convergence is established for a 2D continuous system with an arbitrary domain shape and arbitrary boundary conditions, and it is elaborated in detail for a general rectangular Kirchhoff plate. An example of a rectangular Kirchhoff plate that has three simply supported boundaries and one free boundary with an attached Euler–Bernoulli beam is investigated using the developed method and results are compared with those from other global and local spatial discretization methods. Advantages of the new method over local spatial discretization methods are much fewer DOFs and much less computational effort, and those over the assumed modes method (AMM) are better numerical property, a faster calculation speed, and much higher accuracy in calculation of bending moments and transverse shearing forces that are related to high-order spatial derivatives of the displacement of the plate with an edge beam.

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Accurate Multi-Phase Flow Simulation in Faulted Reservoirs Using Mimetic Finite Difference Methods on Polyhedral Cells

10.2118/206298-ms ◽

2021 ◽

Author(s):

Rencheng Dong ◽

Faruk O. Alpak ◽

Mary F. Wheeler

Keyword(s):

Hybrid Method ◽

Corner Point ◽

Flow Simulation ◽

Phase Flow ◽

Reference Solution ◽

Pressure Equation ◽

Discretization Methods ◽

Multi Phase Flow ◽

Polyhedral Cells ◽

Multi Phase

Abstract Faulted reservoirs are commonly modeled by corner-point grids. Since the two-point flux approximation (TPFA) method is not consistent on non-orthogonal grids, multi-phase flow simulation using TPFA on corner-point grids may have significant discretization errors if grids are not K-orthogonal. To improve the simulation accuracy, we developed a novel method where the faults are modeled by polyhedral cells, and mimetic finite difference (MFD) methods are used to solve flow equations. We use a cut-cell approach to build the mesh for faulted reservoirs. A regular orthogonal grid is first constructed,and then fault planes are added by dividing cells at fault planes. Most cells remain orthogonal while irregular non-orthogonal polyhedral cells can be formed with multiple cell divisions. We investigated three spatial discretization methods for solving the pressure equation on general polyhedral grids, including the TPFA, MFD and TPFA-MFD hybrid methods. In the TPFA-MFD hybrid method, the MFD method is only applied to part of the domain while the TPFA method is applied to rest of the domain. We compared flux accuracy between TPFA and MFD methods by solving a single-phase flow problem. The reference solution is obtained on a rectangular grid while the same problem is solved by TPFA and MFD methods on a grid with distorted cells near a fault. Fluxes computed using TPFA exhibit larger errors in the vicinity of the fault while fluxes computed using MFD are still as accurate as the reference solution. We also compared saturation accuracy of two-phase (oil and water) flow in faulted reservoirs when the pressure equation is solved by different discretization methods. Compared with the reference saturation solution, saturation exhibits non-physical errors near the fault when pressure equation is solved by the TPFA method. Since the MFD method yields accurate fluxes over general polyhedral grids, the resulting saturation solutions match the reference saturation solutions with an enhanced accuracy when the pressure equation is solved by the MFD method. Based on the results of our simulation studies, the accuracy of the TPFA-MFD hybrid method is very close to the accuracy of the MFD method while the TPFA-MFD hybrid method is computationally cheaper than the MFD method.

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Numerical modeling of seismic waves by discontinuous spectral element methods

ESAIM Proceedings and Surveys ◽

10.1051/proc/201861001 ◽

2018 ◽

Vol 61 ◽

pp. 1-37 ◽

Cited By ~ 7

Author(s):

Paola F. Antonietti ◽

Alberto Ferroni ◽

Ilario Mazzieri ◽

Roberto Paolucci ◽

Alfio Quarteroni ◽

...

Keyword(s):

Numerical Modeling ◽

Discontinuous Galerkin ◽

Large Scale ◽

Seismic Waves ◽

Spectral Element ◽

Fully Discrete ◽

Time Marching ◽

Space Discretization ◽

Large Earthquakes

We present a comprehensive review of Discontinuous Galerkin Spectral Element (DGSE) methods on hybrid hexahedral/tetrahedral grids for the numerical modeling of the ground motion induced by large earthquakes. DGSE methods combine the exibility of discontinuous Galerkin meth-ods to patch together, through a domain decomposition paradigm, Spectral Element blocks where high-order polynomials are used for the space discretization. This approach allows local adaptivity on discretization parameters, thus improving the quality of the solution without affecting the compu-tational costs. The theoretical properties of the semidiscrete formulation are also revised, including well-posedness, stability and error estimates. A discussion on the dissipation, dispersion and stability properties of the fully-discrete (in space and time) formulation is also presented. Here space dis-cretization is obtained based on employing the leap-frog time marching scheme. The capabilities of the present approach are demonstrated through a set of computations of realistic earthquake scenar-ios obtained using the code SPEED (http://speed.mox.polimi.it), an open-source code specifically designed for the numerical modeling of large-scale seismic events jointly developed at Politecnico di Milano by The Laboratory for Modeling and Scientific Computing MOX and by the Department of Civil and Environmental Engineering.

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