scholarly journals Performance assessment of low-order versus high-order numerical schemes in the numerical simulation of aquifer flow

2016 ◽  
Vol 47 (6) ◽  
pp. 1104-1115 ◽  
Author(s):  
A. A. Ameli ◽  
M. J. Abedini
Keyword(s):  
Numerical Methods ◽  
Transient Flow ◽  
Exact Analytical Solution ◽  
Differential Quadrature Method ◽  
High Order ◽  
Unconfined Aquifers ◽  
Node Distribution ◽  
Pumping Wells ◽  
Mesh Less ◽  
Low Order

Numerical methods have been widely used to simulate transient groundwater flow induced by pumping wells in geometrically and mathematically complex systems. However, flow and transport simulation using low-order numerical methods can be computationally expensive with a low rate of convergence in multi-scale problems where fine spatial discretization is required to ensure stability and desirable accuracy (for instance, close to a pumping well). Numerical approaches based on high-order test functions may better emulate the global behavior of parabolic and/or elliptic groundwater governing equations with and without the presence of pumping well(s). Here, we assess the appropriateness of high-order differential quadrature method (DQM) and radial basis function (RBF)-DQM approaches compared to low-order finite difference and finite element methods. This assessment is carried out using the exact analytical solution by Theis and observed head data as benchmarks. Numerical results show that high-order DQM and RBF-DQM are more efficient schemes compared to low-order numerical methods in the simulation of 1-D axisymmetric transient flow induced by a pumping well. Mesh-less RBF-DQM, with the ability to implement arbitrary (e.g., adaptive) node distribution, properly simulates 2-D transient flow induced by pumping wells in confined/unconfined aquifers with regular and irregular geometries, compared to the other high-order and low-order approaches presented in this paper.

scholarly journals Coupling of hybridisable discontinuous Galerkin and finite volumes for transient compressible flows

2021 ◽  
Author(s):  
◽  
Sanjay Komala Sheshachala
Keyword(s):  
Discontinuous Galerkin ◽  
Compressible Flows ◽  
Transient Flow ◽  
Degree Of Approximation ◽  
High Order ◽  
Finite Volumes ◽  
Implicit Time ◽  
Wind Gust ◽  
Transient Effects ◽  
Low Order

Fast, high-fidelity solution workflows for transient flow phenomena is an important challenge in the computational fluid dynamics (CFD) community. Current low-order methodologies suffer from large dissipation and dispersion errors and require large mesh sizes for unsteady flow simulations. Recently, on the other hand, high-order methods have gained popularity offering high solution accuracy. But they suffer from the lack of robust, curvilinear mesh generators.A novel methodology that combines the advantages of the classical vertex-centred finite volume (FV) method and high-order hybridisable discontinuous Galerkin (HDG) method is presented for the simulation of transient inviscid compressible flows. The resulting method is capable of simulating the transient effects on coarse, unstructured meshes that are suitable to perform steady simulations with traditional low-order methods. In the vicinity of the aerodynamic shapes, FVs are used whereas in regions where the size of the element is too large for finite volumes to provide an accurate answer, the high-order HDG approach is employed with a non-uniform degree of approximation. The proposed method circumvents the need to produce tailored meshes for transient simulations, as required in a low-order context, and also the need to produce high-order curvilinear meshes, as required by high-order methods.FV and HDG methods for compressible inviscid flows with an implicit time-stepping method and capable of handling flow discontinuities is developed. A two-way coupling of the methods in a monolithic manner was achieved by the consistent application of the so-called transmission conditions at the FV-HDG interface. Numerical tests highlight the optimal convergence properties of the coupled HDG-FV scheme. Numeri-cal examples demonstrate the potential and suitability of the developed methodology for unsteady 2D and 3D flows in the context of simulating the wind gust effect on aerodynamic shapes.

On the Accurate Prediction of Tip Vortex: Effect of Numerical Schemes

2013 ◽  
Author(s):  
Xinrong Su ◽  
Satoru Yamamoto ◽  
Xin Yuan
Keyword(s):  
Numerical Methods ◽  
Numerical Scheme ◽  
High Order ◽  
Accurate Prediction ◽  
Upwind Scheme ◽  
Tip Vortex ◽  
Vortical Flow ◽  
Order Scheme ◽  
Central Scheme ◽  
Low Order

This work is conducted towards the accurate prediction of compressor tip vortex. Accurate computation of highly vortical flow is affected by many parameters, such as numerical scheme and turbulence model. In this work the effect of numerical scheme is studied using mesh refinement study and comparison of numerical results from central scheme and a newly developed high order upwind scheme. Behaviors of numerical methods in the tip vortex region are also theoretically and numerically analyzed. It is found the computed tip vortex is significantly affected by mesh resolution and numerical dissipation. Currently widely numerical strategy, i.e., mesh with moderate resolution and low order scheme would yield quite inaccurate result. Predicted tip vortex is always dissipated earlier and this highlights the advantage of high order scheme in predicting detailed flow features. Besides coarser mesh and low order method, analysis of numerical methods reveals a new finding, in that the designed order of accuracy is not guaranteed in the tip vortex region. For central scheme pressure based shock sensor is unnecessarily activated and excessive artificial dissipation is added. For high order upwind scheme it tends to use low order reconstruction and new method considering flow physics shows its improved vortex prediction capability. Conclusions from this work can be used in future numerical studies about tip vortex to improve the numerical accuracy.

Optimization of the Navy’s three-dimensional mine impact burial prediction simulation model, Impact35, using high-order numerical methods

2021 ◽  
pp. 154851292110286
Author(s):  
Athanasios Donas ◽  
Ioannis Famelis ◽  
Peter C Chu ◽  
George Galanis
Keyword(s):  
Numerical Analysis ◽  
Numerical Methods ◽  
Prediction Model ◽  
Simulation Model ◽  
Three Dimensional ◽  
Simulation System ◽  
High Order ◽  
Alternative Methodology ◽  
Runge Kutta ◽  
Fifth Order

The aim of this paper is to present an application of high-order numerical analysis methods to a simulation system that models the movement of a cylindrical-shaped object (mine, projectile, etc.) in a marine environment and in general in fluids with important applications in Naval operations. More specifically, an alternative methodology is proposed for the dynamics of the Navy’s three-dimensional mine impact burial prediction model, Impact35/vortex, based on the Dormand–Prince Runge–Kutta fifth-order and the singly diagonally implicit Runge–Kutta fifth-order methods. The main aim is to improve the time efficiency of the system, while keeping the deviation levels of the final results, derived from the standard and the proposed methodology, low.

Polynomial Moving Fitting Method for Edge Identification

2011 ◽  
Vol 308-310 ◽  
pp. 2560-2564 ◽  
Author(s):  
Xiang Rong Yuan
Keyword(s):  
Edge Detection ◽  
Curve Fitting ◽  
Polynomial Function ◽  
High Order ◽  
Polynomial Fitting ◽  
Fitting Method ◽  
Order Polynomial ◽  
Better Than ◽  
Low Order

A moving fitting method for edge detection is proposed in this work. Polynomial function is used for the curve fitting of the column of pixels near the edge. Proposed method is compared with polynomial fitting method without sub-segment. The comparison shows that even with low order polynomial, the effects of moving fitting are significantly better than that with high order polynomial fitting without sub-segment.

Numerical methods with a high order of accuracy applied in the quantum system

1996 ◽  
Vol 104 (6) ◽  
pp. 2275-2286 ◽  
Author(s):  
Wusheng Zhu ◽  
Xinsheng Zhao ◽  
Youqi Tang
Keyword(s):  
Numerical Methods ◽  
Quantum System ◽  
High Order ◽  
Order Of Accuracy ◽  
High Order Of Accuracy

scholarly journals Stability of Soliton Solutions For A PT- Symmetric NLDC Considering High-Order Dispersion and Nonlinear Effects Simultaneously

2021 ◽  
Author(s):  
Lida Safaei ◽  
Mohsen Hatami ◽  
Mahmood Borhani Zarandi
Keyword(s):  
Communication Systems ◽  
Exact Analytical Solution ◽  
Nonlinear Effects ◽  
High Order ◽  
Order Effects ◽  
Coupled Equations ◽  
Solitary Solutions ◽  
Stability And Instability ◽  
The Stability ◽  
Order Dispersion

Abstract In this paper, we analytically solve the coupled equations of a PT -Symmetric NLDC by considering high-order dispersion and nonlinear effects (Raman Scattering and self-steeping) simultaneously in normal dispersion regime. To the best of knowledge no works has been done in previous studies to decoupled these equations and obtain an exact analytical solution. The new exact bright solitary solutions are derived. In addition, to study the stability and instability of these propagated solitons in a PT -Symmetric NLDC, perturbation theory is used. Numerical methods are applied to find perturbed eigenvalues and eigenfunctions. The Stability of obtained four perturbed eigenvalues and perturbed eigenfunctions for a PT -Symmetric NLDC equations regard to high-order effects are examined. Using these results and simulating the propagation of perturbed temporal bright solitons through PT -Symmetric NLDC show that perturbed solitons are mostly stable. This means that high-order dispersion and nonlinear effects canceled each other and do not affected the propagated solitons. Furthermore, the evolution of perturbed solitons energies match well the previous results and con rmed the stability of these solitons in a PT -Symmetric NLDC. As seen the energies of pulses in bar and cross behave in two manner 1) the exchange of energy is happened in some periods, but the shape of each pulse in bar and cross is preserved. Therefore, the solitons under this eigenfunction perturbation are mostly stable. 2) the evolution of energy in the bar and cross, demonstrate that there is no changes in their energies and they remain constant. It is straightforward to show that in spite of considering high-order effects, the perturbed soliton conserve the shape and it remain stable. The deliverables of this article not only demonstrate a novel approach to ultra-fast pulses, solitons and optical couplers, but more fundamentally, they could give insight for improving the new medical equipments technologies, enabling innovations in nonlinear optics and their usage in designing new communication systems and Photonic devices.

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