scholarly journals A free-boundary model of diffusive valley growth: theory and observation

2017 ◽  
Vol 473 (2202) ◽  
pp. 20170159 ◽  
Author(s):  
Robert Yi ◽  
Yossi Cohen ◽  
Hansjörg Seybold ◽  
Eric Stansifer ◽  
Robb McDonald ◽  
...  
Keyword(s):  
Theoretical Model ◽  
Free Boundary ◽  
Moving Boundary ◽  
Three Dimensions ◽  
Growth Theory ◽  
Variable Diffusivity ◽  
Boundary Model ◽  
New Feature ◽  
Underlying Processes

Valleys that form around a stream head often develop characteristic finger-like elevation contours. We study the processes involved in the formation of these valleys and introduce a theoretical model that indicates how shape may inform the underlying processes. We consider valley growth as the advance of a moving boundary travelling forward purely through linearly diffusive erosion, and we obtain a solution for the valley shape in three dimensions. Our solution compares well to the shape of slowly growing groundwater-fed valleys found in Bristol, Florida. Our results identify a new feature in the formation of groundwater-fed valleys: a spatially variable diffusivity that can be modelled by a fixed-height moving boundary.

scholarly journals Meshless Local Petrov–Galerkin Formulation of Inverse Stefan Problem via Moving Least Squares Approximation

2019 ◽  
Vol 24 (4) ◽  
pp. 101
Author(s):  
A. Karami ◽  
Saeid Abbasbandy ◽  
E. Shivanian
Keyword(s):  
Free Boundary ◽  
Least Squares ◽  
Boundary Problem ◽  
Moving Boundary ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Moving Least Squares ◽  
Heaviside Step Function ◽  
Mlpg Method ◽  
Mls Approximation

In this paper, we study the meshless local Petrov–Galerkin (MLPG) method based on the moving least squares (MLS) approximation for finding a numerical solution to the Stefan free boundary problem. Approximation of this problem, due to the moving boundary, is difficult. To overcome this difficulty, the problem is converted to a fixed boundary problem in which it consists of an inverse and nonlinear problem. In other words, the aim is to determine the temperature distribution and free boundary. The MLPG method using the MLS approximation is formulated to produce the shape functions. The MLS approximation plays an important role in the convergence and stability of the method. Heaviside step function is used as the test function in each local quadrature. For the interior nodes, a meshless Galerkin weak form is used while the meshless collocation method is applied to the the boundary nodes. Since MLPG is a truly meshless method, it does not require any background integration cells. In fact, all integrations are performed locally over small sub-domains (local quadrature domains) of regular shapes, such as intervals in one dimension, circles or squares in two dimensions and spheres or cubes in three dimensions. A two-step time discretization method is used to deal with the time derivatives. It is shown that the proposed method is accurate and stable even under a large measurement noise through several numerical experiments.

Numerical Solution of a Nonlinear Diffusion Model for Soybean Hydration with Moving Boundary

2015 ◽  
Vol 11 (5) ◽  
pp. 587-595 ◽  
Author(s):  
Douglas J. Nicolin ◽  
Gisleine E. C. da Silva ◽  
Regina Maria M. Jorge ◽  
Luiz Mario M. Jorge
Keyword(s):  
Differential Equation ◽  
Diffusion Model ◽  
Nonlinear Diffusion ◽  
Numerical Scheme ◽  
Moving Boundary ◽  
Grid Method ◽  
Variable Diffusivity ◽  
Variable Space ◽  
Diffusive Fluxes ◽  
Moisture Profiles

Abstract Variable diffusivity and volume of the grains are taken into account in the diffusion model that describes mass transfer in soybean hydration. The variable space grid method (VSGM) was used to consider the increase in grain size, and the diffusivity was considered an exponential function of the moisture content. An equation for the behavior of the grain radius as a function of time was obtained by global mass balance over the soybean grain and the differential equation considered that the increase in radius happens due to the influence of the convective and diffusive fluxes at the surface of the grains. The model was solved by an explicit numerical scheme which presented satisfactory results. The results showed the behavior of moisture profiles obtained as a function of time and radial position and also showed how the grain radius increased with time and changed the solution domain of the diffusion equation.

Dynamic Simulation of an Organic Rankine Cycle (ORC) System Driven by Exhaust

2015 ◽  
Vol 738-739 ◽  
pp. 986-990
Author(s):  
Zhi Gang Wang ◽  
Jia Guang Cheng ◽  
Yan Wang ◽  
Qiang Shen
Keyword(s):  
Low Temperature ◽  
Control Strategy ◽  
Fossil Fuels ◽  
Moving Boundary ◽  
Organic Rankine Cycle ◽  
Rankine Cycle ◽  
Energy Crisis ◽  
Transient Phenomena ◽  
Simulation Results ◽  
Boundary Model

Organic Rankine Cycle (ORC) is one of the most promising technologies for low-temperature energy conversion. In recent years, it has gotten more attention due to the energy crisis and environmental problems caused by the combustion of fossil fuels. In this paper, a moving boundary model is introduced to describe the transient phenomena of evaporator and condenser, which are the important components of ORC. The simulation results are given to illustrate the efficiency and feasibility of the proposed control strategy.

Quasi Trefftz Spectral Method for Stokes Problem

1997 ◽  
Vol 07 (08) ◽  
pp. 1187-1212 ◽  
Author(s):  
S. A. Lifits ◽  
S. Yu. Reutskiy ◽  
G. Pontrelli ◽  
B. Tirozzi
Keyword(s):  
Free Boundary ◽  
Spectral Method ◽  
Initial Value Problems ◽  
Moving Boundary ◽  
Stokes Problem ◽  
Boundary Value ◽  
Elliptic Operators ◽  
Initial Value ◽  
Primitive Variables

A new numerical Quasi Trefftz Spectral Method (QTSM) which was earlier suggested for solving boundary value and initial value problems with elliptic operators is applied to linear stationary hydrodynamic problems. The primitive variables [Formula: see text] are used. The method has been found to work well for different problems, including free boundary ones. The problem of the Stefan type in the domain with moving boundary is also considered. The possibilities of further developments of QTSM are discussed.

Iterative Part Design With a Virtual Reality Interface

1996 ◽  
Author(s):  
S. N. Trika ◽  
P. Banerjee ◽  
R. L. Kashyap
Keyword(s):  
Virtual Reality ◽  
Computer Aided Design ◽  
Three Dimensions ◽  
Mechanical Parts ◽  
Cad System ◽  
Current State ◽  
Feature Based ◽  
New Feature ◽  
Feature Based Design ◽  
Aided Design

Abstract A virtual reality (VR) interface to a feature-based computer-aided design (CAD) system promises to provide a simple interface to a designer of mechanical parts, because it allows intuitive specification of design features such as holes, slots, and protrusions in three-dimensions. Given the current state of a part design, the designer is free to navigate around the part and in part cavities to specify the next feature. This method of feature specification also provides directives to the process-planner regarding the order in which the features may be manufactured. In iterative feature-based design, the existing part cavities represent constraints as to where the designer is allowed to navigate and place the new feature. The CAD system must be able to recognize the part cavities and enforce these constraints. Furthermore, the CAD system must be able to update its knowledge of part cavities when the new feature is added. In this paper, (i) we show how the CAD system can enforce the aforementioned constraints by exploiting the knowledge of part cavities and their adjacencies, and (ii) present efficient methods for updates of the set of part cavities when the designer adds a new feature.

scholarly journals A sharp-front moving boundary model for malignant invasion

2020 ◽  
Vol 412 ◽  
pp. 132639 ◽  
Author(s):  
Maud El-Hachem ◽  
Scott W. McCue ◽  
Matthew J. Simpson
Keyword(s):  
Moving Boundary ◽  
Boundary Model ◽  
Sharp Front
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