Numerical oscillation in seepage analysis of unsaturated soils

2001 ◽  
Vol 38 (3) ◽  
pp. 639-651 ◽  
Author(s):  
Muthusamy Karthikeyan ◽  
Thiam-Soon Tan ◽  
Kok-Kwang Phoon
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Unsaturated Soil ◽  
Unsaturated Soils ◽  
Heat Diffusion ◽  
Step Size ◽  
Time Step ◽  
Seepage Analysis ◽  
Time Step Size ◽  
Element Method

The finite element method provides a popular means of analyzing groundwater flow in an unsaturated soil. In such problems, oscillatory results are often observed in the finite element solution. Such a phenomenon is observed, for example, when a typical finite element program such as Seep/w is used to model water infiltration into unsaturated soils. Numerical oscillations are often found near the wetting front where the hydraulic gradient is the steepest. These oscillations do not always reduce with decreasing or increasing time-step size alone; rather, an appropriate ratio between time-step size and element size is required. As the pore-water pressures predicted from a transient seepage analysis are used as input groundwater conditions for other types of analysis such as slope stability, contaminant transport, and capillary barrier, these oscillations may have important practical ramifications. Since seepage analysis is common in engineering practice, it is important that appropriate criteria are identified to minimize, if not to remove, the oscillations. In this paper, numerical examples are provided to demonstrate that a simple set of criteria, developed in heat diffusion problems with constant properties to control oscillation, is also applicable to one- and two-dimensional unsaturated seepage analyses, for a range of material nonlinearities that are frequently encountered in unsaturated soils.Key words: unsaturated soil, soil-water characteristic curve, seepage analysis, finite element method, numerical oscillation.

Finite-Element Method Applied to Heat Conduction in Solids with Nonlinear Boundary Conditions

1973 ◽  
Vol 95 (1) ◽  
pp. 126-129 ◽  
Author(s):  
R. E. Beckett ◽  
S.-C. Chu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Heat Conduction ◽  
Boundary Conditions ◽  
Transient Heat Conduction ◽  
Nonlinear Boundary Conditions ◽  
Step Size ◽  
Time Step ◽  
Time Step Size ◽  
Element Method

By use of an implicit iteration technique, the finite-element method applied to the heat-conduction problems of solids is no longer restricted to the linear heat-flux boundary conditions, but is extended to include nonlinear radiation–convection boundary conditions. The variation of surface temperatures within each time increment is taken into account; hence a rather large time-step size can be assigned to obtain transient heat-conduction solutions without introducing instability in the surface temperature of a body.

A finite element method for the Navier-Stokes equations in moving domain with application to hemodynamics of the left ventricle

2017 ◽  
Vol 32 (4) ◽  
Author(s):  
Alexander Danilov ◽  
Alexander Lozovskiy ◽  
Maxim Olshanskii ◽  
Yuri Vassilevski
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Left Ventricle ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Time Step ◽  
Navier Stokes Equations ◽  
Computed Tomography Images ◽  
Time Dependent Domain ◽  
Element Method

AbstractThe paper introduces a finite element method for the Navier-Stokes equations of incompressible viscous fluid in a time-dependent domain. The method is based on a quasi-Lagrangian formulation of the problem and handling the geometry in a time-explicit way. We prove that numerical solution satisfies a discrete analogue of the fundamental energy estimate. This stability estimate does not require a CFL time-step restriction. The method is further applied to simulation of a flow in a model of the left ventricle of a human heart, where the ventricle wall dynamics is reconstructed from a sequence of contrast enhanced Computed Tomography images.

scholarly journals APPLICATION OF GALERKIN FINITE ELEMENT METHOD IN THE SOLUTION OF 3D DIFFUSION IN SOLIDS

2009 ◽  
Vol 8 (2) ◽  
pp. 79 ◽  
Author(s):  
E. C. Romão ◽  
M. D. De Campos ◽  
J. A. Martins ◽  
L. F. M. De Moura
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Solution ◽  
Heat Diffusion ◽  
Average Error ◽  
Galerkin Finite Element Method ◽  
Diffusion In Solids ◽  
Galerkin Finite Element ◽  
L2 Norm ◽  
Element Method

This paper presents the numerical solution by the Galerkin Finite Element Method, on the three-dimensional Laplace and Helmholtz equations, which represent the heat diffusion in solids. For the two applications proposed, the analytical solutions found in the literature review were used in comparison with the numerical solution. The results analysis was made based on the the L2 Norm (average error throughout the domain) and L¥ Norm (maximum error in the entire domain). The two application results, one of the Laplace equation and the Helmholtz equation, are presented and discussed in order to to test the efficiency of the method.

Nonlinear Random Responses of Shell Structures With Spatial Uncertainties

2002 ◽  
Author(s):  
C. W. S. To
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Large Deformation ◽  
Mass Matrix ◽  
Spatial Uncertainty ◽  
Shell Structures ◽  
Time Step ◽  
Central Difference ◽  
Approximation Techniques ◽  
Element Method

A novel procedure for large deformation nonstationary random response computation of shell structures with spatial uncertainty is presented. The procedure is free from the limitations associated with those employing perturbation approximation techniques, such as the so-called stochastic finite element method and probabilistic finite element method, for systems with spatial uncertainties. In addition, the procedure has several important and excellent features. Chief among these are: (a) ability to deal with large deformation problems of finite strain and finite rotation; (b) application of explicit linear and nonlinear element stiffness matrices, mass matrix, and load vectors reduces computation time drastically; (c) application of the averaged deterministic central difference scheme for the updating of co-ordinates and element matrices at every time step makes it extremely efficient compared with those employing the Monte Carlo simulation and the conventional central difference algorithm; and (d) application of the time co-ordinate transformation enables one to study highly stiff structural systems.

scholarly journals A global finite-element shallow-water model supporting continuous and discontinuous elements

2014 ◽  
Vol 7 (6) ◽  
pp. 3017-3035 ◽  
Author(s):  
P. A. Ullrich
Keyword(s):  
Finite Element ◽  
Shallow Water ◽  
Wave Train ◽  
Correction Function ◽  
Water Model ◽  
Step Size ◽  
Time Step ◽  
Time Step Size ◽  
Discontinuous Elements ◽  
Cubed Sphere

Abstract. This paper presents a novel nodal finite-element method for either continuous and discontinuous elements, as applied to the 2-D shallow-water equations on the cubed sphere. The cornerstone of this method is the construction of a robust derivative operator that can be applied to compute discrete derivatives even over a discontinuous function space. A key advantage of the robust derivative is that it can be applied to partial differential equations in either a conservative or a non-conservative form. However, it is also shown that discontinuous penalization is required to recover the correct order of accuracy for discontinuous elements. Two versions with discontinuous elements are examined, using either the g1 and g2 flux correction function for distribution of boundary fluxes and penalty across nodal points. Scalar and vector hyperviscosity (HV) operators valid for both continuous and discontinuous elements are also derived for stabilization and removal of grid-scale noise. This method is validated using four standard shallow-water test cases, including geostrophically balanced flow, a mountain-induced Rossby wave train, the Rossby–Haurwitz wave and a barotropic instability. The results show that although the discontinuous basis requires a smaller time step size than that required for continuous elements, the method exhibits better stability and accuracy properties in the absence of hyperviscosity.

A Finite Element Method for a Nonlinear Sloshing Problem

2003 ◽  
Author(s):  
J. H. Kyoung ◽  
J. W. Kim ◽  
K. J. Bai
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Free Surface ◽  
Impact Load ◽  
Surface Condition ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Time Step ◽  
Nonlinear Sloshing ◽  
Element Method

A nonlinear sloshing problem in LNG tanker is numerically simulated. During excessive sloshing, the sloshing-induced impact load can cause a critical damage on the tank structure. Recently, this problem became one of important issues in FPSO design. A three-dimensional free surface flow in a tank is formulated in the scope of potential flow theory. The exact nonlinear free surface condition is satisfied numerically. A finite-element method based on Hamilton’s principle is employed as a numerical scheme. The problem is treated as an initial-value problem. The computations are made through an iterative method at each time step. The hydrodynamic loading on the pillar in the tank is computed and compared with other results.

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