scholarly journals Numerical modeling of tectonic underplating in accretionary wedge systems

Geosphere ◽  
2020 ◽  
Vol 16 (6) ◽  
pp. 1385-1407
Author(s):  
Jonas B. Ruh
Keyword(s):  
Numerical Modeling ◽  
Numerical Experiments ◽  
Flexural Rigidity ◽  
Structural Evolution ◽  
Surface Erosion ◽  
Accretionary Wedge ◽  
Sediment Accretion ◽  
First Order ◽  
Rear Part ◽  
Horizontal Growth

Abstract Many fossil and active accretionary wedge systems show signs of tectonic underplating, which denotes accretion of underthrust material to the base of the wedge. Underplating is a viable process for thickening of the rear part of accretionary wedges, for example as a response to horizontal growth perpendicular to strike. Here, numerical experiments with a visco-elasto-plastic rheology are applied to test the importance of backstop geometry, flexural rigidity, décollement strength, and surface erosion on the structural evolution of accretionary wedges undergoing different modes of sediment accretion, where underplating is introduced by the implementation of two, a basal and an intermediate, décollement levels. Results demonstrate that intense erosion and a strong lower plate hamper thickening of a wedge at the rear, enhancing localized underplating, antiformal stacking, and subsequent exhumation to sustain its critical taper. Furthermore, large strength contrasts between basal and intermediate décollements have an important morphological impact on wedge growth due to different resulting critical taper angles. Presented numerical experiments are compared to natural examples of accretionary wedges and are able to recreate first-order structural observations related to underplating.

scholarly journals Virtual Element Method for the Laplace-Beltrami equation on surfaces

2018 ◽  
Vol 52 (3) ◽  
pp. 965-993 ◽  
Author(s):  
Massimo Frittelli ◽  
Ivonne Sgura
Keyword(s):  
Numerical Experiments ◽  
Beltrami Equation ◽  
Convergence Result ◽  
Point Of View ◽  
Polygonal Approximation ◽  
Virtual Element Method ◽  
Element Space ◽  
First Order ◽  
Virtual Element ◽  
Element Method

We present and analyze a Virtual Element Method (VEM) for the Laplace-Beltrami equation on a surface in ℝ3, that we call Surface Virtual Element Method (SVEM). The method combines the Surface Finite Element Method (SFEM) (Dziuk, Eliott, G. Dziuk and C.M. Elliott., Acta Numer. 22 (2013) 289–396.) and the recent VEM (Beirão da Veiga et al., Math. Mod. Methods Appl. Sci. 23 (2013) 199–214.) in order to allow for a general polygonal approximation of the surface. We account for the error arising from the geometry approximation and in the case of polynomial order k = 1 we extend to surfaces the error estimates for the interpolation in the virtual element space. We prove existence, uniqueness and first order H1 convergence of the numerical solution.We highlight the differences between SVEM and VEM from the implementation point of view. Moreover, we show that the capability of SVEM of handling nonconforming and discontinuous meshes can be exploited in the case of surface pasting. We provide some numerical experiments to confirm the convergence result and to show an application of mesh pasting.

scholarly journals Stabilised explicit Adams-type methods

2021 ◽  
pp. 82-98
Author(s):  
Vasily I. Repnikov ◽  
Boris V. Faleichik ◽  
Andrew V. Moisa
Keyword(s):  
Numerical Experiments ◽  
Step Method ◽  
Type Method ◽  
Constrained Optimisation ◽  
First Order ◽  
Error Constant ◽  
Stability Intervals ◽  
Multi Step Methods ◽  
First Order Methods ◽  
Accuracy And Stability

In this work we present explicit Adams-type multi-step methods with extended stability intervals, which are analogous to the stabilised Chebyshev Runge – Kutta methods. It is proved that for any k ≥ 1 there exists an explicit k-step Adams-type method of order one with stability interval of length 2k. The first order methods have remarkably simple expressions for their coefficients and error constant. A damped modification of these methods is derived. In the general case, to construct a k-step method of order p it is necessary to solve a constrained optimisation problem in which the objective function and p constraints are second degree polynomials in k variables. We calculate higher-order methods up to order six numerically and perform some numerical experiments to confirm the accuracy and stability of the methods.

scholarly journals Numerical Study on Phase-Fitted and Amplification-Fitted Diagonally Implicit Two Derivative Runge-Kutta Method for Periodic IVPS

2021 ◽  
Vol 50 (6) ◽  
pp. 1799-1814
Author(s):  
Norazak Senu ◽  
Nur Amirah Ahmad ◽  
Zarina Bibi Ibrahim ◽  
Mohamed Othman
Keyword(s):  
Fourth Order ◽  
Initial Value Problems ◽  
Numerical Experiments ◽  
Numerical Study ◽  
Kutta Method ◽  
Initial Value ◽  
First Order ◽  
Runge Kutta Method ◽  
Runge Kutta ◽  
The Stability

A fourth-order two stage Phase-fitted and Amplification-fitted Diagonally Implicit Two Derivative Runge-Kutta method (PFAFDITDRK) for the numerical integration of first-order Initial Value Problems (IVPs) which exhibits periodic solutions are constructed. The Phase-Fitted and Amplification-Fitted property are discussed thoroughly in this paper. The stability of the method proposed are also given herewith. Runge-Kutta (RK) methods of the similar property are chosen in the literature for the purpose of comparison by carrying out numerical experiments to justify the accuracy and the effectiveness of the derived method.

scholarly journals Weak solvability of the unconditionally stable difference scheme for the coupled sine-Gordon system

2020 ◽  
Vol 25 (6) ◽  
pp. 997-1014
Author(s):  
Ozgur Yildirim ◽  
Meltem Uzun
Keyword(s):  
Difference Scheme ◽  
Numerical Method ◽  
Existence And Uniqueness ◽  
Numerical Experiments ◽  
Finite Difference Schemes ◽  
Order Of Accuracy ◽  
Unconditionally Stable ◽  
First Order ◽  
The Difference ◽  
Weak Solvability

In this paper, we study the existence and uniqueness of weak solution for the system of finite difference schemes for coupled sine-Gordon equations. A novel first order of accuracy unconditionally stable difference scheme is considered. The variational method also known as the energy method is applied to prove unique weak solvability.We also present a new unified numerical method for the approximate solution of this problem by combining the difference scheme and the fixed point iteration. A test problem is considered, and results of numerical experiments are presented with error analysis to verify the accuracy of the proposed numerical method.

scholarly journals Numerical modeling of the tide in the coast ar-ea Casablanca-Mohammedia (Morocco)

2017 ◽  
Vol 5 (1) ◽  
pp. 31
Author(s):  
Laila Mouakkir ◽  
Soumia Mordane
Keyword(s):  
Numerical Modeling ◽  
Coastal Area ◽  
Earth Rotation ◽  
Numerical Experiments ◽  
Bottom Topography ◽  
Dynamical Equations ◽  
Motion Equations ◽  
Tidal Circulation ◽  
The Earth ◽  
First Results

The objective of this study is to simulate the tidal circulation in the coastal area Casablanca-Mohammedia located on the Moroccan Atlantic. Simulations of the tidal currents of this zone use the 2D version of the MECCA (Model for Estuarine and Coastal Circulation Assessment). These simulations are based on the depth-integrated dynamical equations of turbulent motion. Equations are solved by using the implicit finite-differences techniques. The modelincorporates the actual bottom topography and the effects of the Earth rotation. As forcing mechanism, the model uses the tidal heights prescribed along the open boundaries.As first results, numerical experiments show that the model provides good results compared to those of the altymetric model TPXO.

A new difference scheme for time fractional heat equations based on the Crank-Nicholson method

2013 ◽  
Vol 16 (4) ◽  
Author(s):  
Ibrahim Karatay ◽  
Nurdane Kale ◽  
Serife Bayramoglu
Keyword(s):  
Diffusion Equation ◽  
Heat Equation ◽  
Difference Scheme ◽  
Numerical Solution ◽  
Caputo Derivative ◽  
Numerical Experiments ◽  
Time Derivative ◽  
Heat Equations ◽  
First Order ◽  
Fractional Heat Equation

AbstractIn this paper, we consider the numerical solution of a time-fractional heat equation, which is obtained from the standard diffusion equation by replacing the first-order time derivative with the Caputo derivative of order α, where 0 < α < 1. The main purpose of this work is to extend the idea on the Crank-Nicholson method to the time-fractional heat equations. By the method of the Fourier analysis, we prove that the proposed method is stable and the numerical solution converges to the exact one with the order O(τ 2-α + h 2), conditionally. Numerical experiments are carried out to support the theoretical claims.

Numerical Modeling of Two Phase Flow under Centrifugation

2012 ◽  
Vol 326-328 ◽  
pp. 221-226
Author(s):  
Jozef Kačur ◽  
Benny Malengier ◽  
Pavol Kišon
Keyword(s):  
Inverse Problem ◽  
Numerical Modeling ◽  
Numerical Experiments ◽  
Two Phase Flow ◽  
Phase Flow ◽  
Two Phase ◽  
Saturated Sample ◽  
Dae Systems ◽  
Capillary Pressure Curves ◽  
Wetting Liquid

Numerical modeling of two-phase flow under centrifugation is presented in 1D.A new method is analysed to determine capillary-pressure curves. This method is based onmodeling the interface between the zone containing only wetting liquid and the zone containingwetting and non wetting liquids. This interface appears when into a fully saturated sample withwetting liquid we inject a non-wetting liquid. By means of this interface an efficient and correctnumerical approximation is created based upon the solution of ODE and DAE systems. Bothliquids are assumed to be immiscible and incompressible. This method is a good candidate tobe used in solution of inverse problem. Some numerical experiments are presented.

scholarly journals Control of a surface of discontinuity in continuous thickness

1992 ◽  
Vol 33 (3) ◽  
pp. 269-289 ◽  
Author(s):  
N. G. Barton ◽  
C.-H. Li ◽  
S. J. Spencer
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Numerical Experiments ◽  
Mineral Processing ◽  
Control Variables ◽  
Partial Differential ◽  
First Order ◽  
And Control

AbstractThis paper examines the control of an interface between a suspension of sedimenting particles in liquid and a bed of dense-packed particles at the bottom of the suspension. The problem arises in the operation of continuous thickeners (e.g. in mineral processing) and is here mathematically described by a first order inhomogeneous partial differential equation for the concentration C(x, t) of particles. The controlled variable is the height H* of the bed, and the control variables are the volume fluxes injected at the feed level and removed at the bed. A strategy to control the interface is devised, and control is confirmed and demonstrated by a series of numerical experiments.

A finite-difference method for the numerical solution of the Sal’nikov thermokinetic oscillator problem

1995 ◽  
Vol 449 (1936) ◽  
pp. 255-271
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Stationary Point ◽  
Difference Method ◽  
Numerical Experiments ◽  
Euler Method ◽  
Initial Value ◽  
First Order ◽  
Highly Nonlinear ◽  
Implicit Finite Difference

A finite-difference method is developed for solving two coupled, ordinary differential equations that model a sequence of chemical reactions. The initial-value problem is highly nonlinear and involves three parameters. Various types of theoretical solution of this problem (the Sal’nikov thermokinetic oscillator problem) may be found, depending on these parameters; this is because the stationary point is surrounded by up to two limit cycles. The well-known, first-order, explicit Euler method and an implicit finite difference method of the same order are used to compute the solution. It is shown that this implicit method may, in fact, be used explicitly and extensive numerical experiments are made to confirm the superior stability properties of the alternative method.

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