Moving boundary truncated grid method for electronic nonadiabatic dynamics

2022 ◽  
Author(s):  
Chun-Yaung Lu ◽  
Tsung-Yen Lee ◽  
Chia-Chun Chou
Keyword(s):  
Moving Boundary ◽  
Grid Method ◽  
Nonadiabatic Dynamics

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.

Solving moving boundary problems with an adaptive moving grid method

1998 ◽  
Vol 53 (19) ◽  
pp. 3393-3411 ◽  
Author(s):  
Jörg Frauhammer ◽  
Harald Klein ◽  
Gerhart Eigenberger ◽  
Ulrich Nowak
Keyword(s):  
Moving Boundary ◽  
Grid Method ◽  
Moving Boundary Problems ◽  
Moving Grid ◽  
Boundary Problems

Computation of Multi-Passage Cascade Flows With Overset and Deforming Grids

1997 ◽  
Author(s):  
Ismail H. Tuncer ◽  
Wolfgang Sanz
Keyword(s):  
Moving Boundary ◽  
Grid Method ◽  
Navier Stokes ◽  
Computational Results ◽  
Compressor Cascade ◽  
Overset Grid ◽  
Overset Grids ◽  
Overset Grid Method ◽  
Background Grid ◽  
Good Agreement

An overset grid method is applied to the solution of single and multi-passage cascade flows with a compressible Navier-Stokes solver. C-type grids around individual blades are overset onto a Cartesian background grid. Overset grids are allowed to move in time relative to each other as prescribed by the oscillatory plunging motion. The overset grid method uses a simple, robust numerical algorithm to localize moving boundary points and to interpolate solution variables across intergrid boundaries. Computational results and comparisons with single/staggered, deforming grid solutions are presented for in- and out-of-phase multi-passage flows through a compressor cascade. Very good agreement is obtained against the deforming grid solutions.

Numerical solution of Stefan problem with variable space grid method based on mixed finite element/finite difference approach

2017 ◽  
Vol 27 (12) ◽  
pp. 2682-2695 ◽  
Author(s):  
Milos Ivanovic ◽  
Marina Svicevic ◽  
Svetislav Savovic
Keyword(s):  
Finite Element ◽  
Temperature Distribution ◽  
Finite Difference ◽  
Stefan Problem ◽  
Moving Boundary ◽  
Mixed Finite Element ◽  
Grid Method ◽  
Content Type ◽  
Space Grid ◽  
Variable Space

Purpose The purpose of this paper is to improve the accuracy and stability of the existing solutions to 1D Stefan problem with time-dependent Dirichlet boundary conditions. The accuracy improvement should come with respect to both temperature distribution and moving boundary location. Design/methodology/approach The variable space grid method based on mixed finite element/finite difference approach is applied on 1D Stefan problem with time-dependent Dirichlet boundary conditions describing melting process. The authors obtain the position of the moving boundary between two phases using finite differences, whereas finite element method is used to determine temperature distribution. In each time step, the positions of finite element nodes are updated according to the moving boundary, whereas the authors map the nodal temperatures with respect to the new mesh using interpolation techniques. Findings The authors found that computational results obtained by proposed approach exhibit good agreement with the exact solution. Moreover, the results for temperature distribution, moving boundary location and moving boundary speed are more accurate than those obtained by variable space grid method based on pure finite differences. Originality/value The authors’ approach clearly differs from the previous solutions in terms of methodology. While pure finite difference variable space grid method produces stable solution, the mixed finite element/finite difference variable space grid scheme is significantly more accurate, especially in case of high alpha. Slightly modified scheme has a potential to be applied to 2D and 3D Stefan problems.

A Four-Step Fixed-Grid Method for 1D Stefan Problems

2010 ◽  
Vol 132 (11) ◽  
Author(s):  
M. Tadi
Keyword(s):  
Free Boundary ◽  
Moving Boundary ◽  
Free Boundary Problems ◽  
Grid Method ◽  
Moving Boundary Problems ◽  
Boundary Problems ◽  
One Dimensional ◽  
Nonlinear Part ◽  
Stefan Problems ◽  
Fixed Grid

This note is concerned with a fixed-grid finite difference method for the solution of one-dimensional free boundary problems. The method solves for the field variables and the location of the boundary in separate steps. As a result of this decoupling, the nonlinear part of the algorithm involves only a scalar unknown, which is the location of the moving boundary. A number of examples are used to study the applicability of the method. The method is particularly useful for moving boundary problems with various conditions at the front.

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