A continuum theory of surface growth

2010 ◽  
Vol 466 (2123) ◽  
pp. 3135-3152 ◽  
Author(s):  
Neil Hodge ◽  
Panayiotis Papadopoulos
Keyword(s):  
Inertial Frame ◽  
Continuum Theory ◽  
The Body ◽  
Surface Growth ◽  
Governing Equations ◽  
Predictive Capacity ◽  
One Dimensional ◽  
Deformable Bodies ◽  
Material Points ◽  
Well Posed

A continuum theory of surface growth in deformable bodies is presented. The theory employs a decomposition of the deformation and growth processes, which leads to a well-posed set of governing equations. It is argued that an evolving reference configuration is required to track the material points in the body. The balance laws are formulated with respect to a non-inertial frame of reference, which is used to track the motion of the body. A one-dimensional example problem is included to showcase the predictive capacity of the theory.

scholarly journals An Unstructured Finite Volume Method for Incompressible Flows With Complex Immersed Boundaries

2009 ◽  
Author(s):  
Lin Sun ◽  
Sanjay R. Mathur ◽  
Jayathi Y. Murthy
Keyword(s):  
Finite Volume Method ◽  
Finite Volume ◽  
Incompressible Flows ◽  
Simple Algorithm ◽  
Flow Region ◽  
Solid Material ◽  
The Body ◽  
Immersed Boundary ◽  
Material Points ◽  
Volume Method

A numerical method is developed for solving the 3D, unsteady, incompressible flows with immersed moving solids of arbitrary geometrical complexity. A co-located (non-staggered) finite volume method is employed to solve the Navier-Stokes governing equations for flow region using arbitrary convex polyhedral meshes. The solid region is represented by a set of material points with known position and velocity. Faces in the flow region located in the immediate vicinity of the solid body are marked as immersed boundary (IB) faces. At every instant in time, the influence of the body on the flow is accounted for by reconstructing implicitly the velocity the IB faces from a stencil of fluid cells and solid material points. Specific numerical issues related to the non-staggered formulation are addressed, including the specification of face mass fluxes, and corrections to the continuity equation to ensure overall mass balance. Incorporation of this immersed boundary technique within the framework of the SIMPLE algorithm is described. Canonical test cases of laminar flow around stationary and moving spheres and cylinders are used to verify the implementation. Mesh convergence tests are carried out. The simulation results are shown to agree well with experiments for the case of micro-cantilevers vibrating in a viscous fluid.

Design and Research of Flat Micro Heat Pipe with Glass Fiber Wick

2011 ◽  
Vol 483 ◽  
pp. 603-606
Author(s):  
Tian Han ◽  
Xiao Wei Liu ◽  
Chao Wang
Keyword(s):  
Glass Fiber ◽  
Heat Pipe ◽  
Experimental Testing ◽  
Governing Equations ◽  
Maximum Heat ◽  
One Dimensional ◽  
Micro Heat Pipe ◽  
Wick Structure

A kind of flat micro heat pipe with glass fiber wick structure is designed and fabricated. The structure of the wick is presented and also the excellence of the structure is described. For the glass fiber wick, the maximum heat transports is calculated by one-dimensional steady governing equations. Experimental testing is performed for the fabricated micro heat pipe in vacuum. The testing results is presented and analyzed.

Nonboundary Conforming Methods for Large-Eddy Simulations of Biological Flows

2005 ◽  
Vol 127 (5) ◽  
pp. 851-857 ◽  
Author(s):  
Elias Balaras ◽  
Jianming Yang
Keyword(s):  
Body Surface ◽  
Computational Algorithm ◽  
The Body ◽  
Large Eddy Simulations ◽  
Moving Boundaries ◽  
Lagrangian Formulation ◽  
Governing Equations ◽  
Solid Interface ◽  
Large Eddy ◽  
Biological Flows

In the present paper a computational algorithm suitable for large-eddy simulations of fluid/structure problems that are commonly encountered in biological flows is presented. It is based on a mixed Eurelian-Lagrangian formulation, where the governing equations are solved on a fixed grid, which is not aligned with the body surface, and the nonslip conditions are enforced via local reconstructions of the solution near the solid interface. With this strategy we can compute the flow around complex stationary/moving boundaries and at the same time maintain the efficiency and optimal conservation properties of the underlying Cartesian solver. A variety of examples, that establish the accuracy and range of applicability of the method are included.

scholarly journals A new method for solving a class of heat conduction equations

2015 ◽  
Vol 19 (4) ◽  
pp. 1205-1210
Author(s):  
Yi Tian ◽  
Zai-Zai Yan ◽  
Zhi-Min Hong
Keyword(s):  
Monte Carlo ◽  
Heat Conduction ◽  
Dimensional Space ◽  
Variable Coefficients ◽  
Algebraic Equations ◽  
Governing Equations ◽  
One Dimensional ◽  
Sparse System ◽  
Linear Algebraic Equations ◽  
Crank Nicolson

A numerical method for solving a class of heat conduction equations with variable coefficients in one dimensional space is demonstrated. This method combines the Crank-Nicolson and Monte Carlo methods. Using Crank-Nicolson method, the governing equations are discretized into a large sparse system of linear algebraic equations, which are solved by Monte Carlo method. To illustrate the usefulness of this technique, we apply it to two problems. Numerical results show the performance of the present work.

scholarly journals Mathematical analysis of hydrodynamics and tissue deformation inside an isolated solid tumor

2018 ◽  
Vol 45 (2) ◽  
pp. 253-278 ◽  
Author(s):  
Meraj Alam ◽  
Bibaswan Dey ◽  
Sekhar Raja
Keyword(s):  
Solid Tumor ◽  
Solid Phase ◽  
Fluid Motion ◽  
Extracellular Fluid ◽  
Mixture Theory ◽  
Coupled System ◽  
Weak Sense ◽  
Governing Equations ◽  
One Dimensional ◽  
2D And 3D

In this article, we present a biphasic mixture theory based mathematical model for the hydrodynamics of interstitial fluid motion and mechanical behavior of the solid phase inside a solid tumor. The tumor tissue considered here is an isolated deformable biological medium. The solid phase of the tumor is constituted by vasculature, tumor cells, and extracellular matrix, which are wet by a physiological extracellular fluid. Since the tumor is deformable in nature, the mass and momentum equations for both the phases are presented. The momentum equations are coupled due to the interaction (or drag) force term. These governing equations reduce to a one-way coupled system under the assumption of infinitesimal deformation of the solid phase. The well-posedness of this model is shown in the weak sense by using the inf-sup (Babuska?Brezzi) condition and Lax?Milgram theorem in 2D and 3D. Further, we discuss a one-dimensional spherical symmetry model and present some results on the stress fields and energy of the system based on ??2 and Sobolev norms. We discuss the so-called phenomena of ?necrosis? inside a solid tumor using the energy of the system.

scholarly journals A new class of discontinuous solar wind solutions

2020 ◽  
Vol 496 (2) ◽  
pp. 1023-1034
Author(s):  
Bidzina M Shergelashvili ◽  
Velentin N Melnik ◽  
Grigol Dididze ◽  
Horst Fichtner ◽  
Günter Brenn ◽  
...  
Keyword(s):  
Solar Wind ◽  
External Source ◽  
Analytic Solutions ◽  
Governing Equations ◽  
Discontinuous Solutions ◽  
One Dimensional ◽  
Heating Source ◽  
New Class ◽  
Localized Heating ◽  
Physical Quantities

ABSTRACT A new class of one-dimensional solar wind models is developed within the general polytropic, single-fluid hydrodynamic framework. The particular case of quasi-adiabatic radial expansion with a localized heating source is considered. We consider analytical solutions with continuous Mach number over the entire radial domain while allowing for jumps in the flow velocity, density, and temperature, provided that there exists an external source of energy in the vicinity of the critical point that supports such jumps in physical quantities. This is substantially distinct from both the standard Parker solar wind model and the original nozzle solutions, where such discontinuous solutions are not permissible. We obtain novel sample analytic solutions of the governing equations corresponding to both slow and fast winds.

scholarly journals The development of biofilm architecture

2016 ◽  
Vol 472 (2188) ◽  
pp. 20150798 ◽  
Author(s):  
A. C. Fowler ◽  
T. M. Kyrke-Smith ◽  
H. F. Winstanley
Keyword(s):  
Bacterial Biofilm ◽  
Governing Equations ◽  
Biofilm Growth ◽  
One Dimensional ◽  
Direct Numerical Solution ◽  
The Common ◽  
Common Observation ◽  
The Stability ◽  
The One ◽  
A Free Boundary Problem

We extend the one-dimensional polymer solution theory of bacterial biofilm growth described by Winstanley et al . (2011 Proc. R. Soc. A 467 , 1449–1467 ( doi:10.1098/rspa.2010.0327 )) to deal with the problem of the growth of a patch of biofilm in more than one lateral dimension. The extension is non-trivial, as it requires consideration of the rheology of the polymer phase. We use a novel asymptotic technique to reduce the model to a free-boundary problem governed by the equations of Stokes flow with non-standard boundary conditions. We then consider the stability of laterally uniform biofilm growth, and show that the model predicts spatial instability; this is confirmed by a direct numerical solution of the governing equations. The instability results in cusp formation at the biofilm surface and provides an explanation for the common observation of patterned biofilm architectures.

scholarly journals Study of Unsteady Flow in a Heat Exchanger by the Method of Characteristics

1992 ◽  
Vol 114 (4) ◽  
pp. 459-463 ◽  
Author(s):  
Yuan Mao Huang
Keyword(s):  
Heat Exchanger ◽  
Unsteady Flow ◽  
Transfer Rate ◽  
Method Of Characteristics ◽  
Governing Equations ◽  
One Dimensional ◽  
The Method Of Characteristics ◽  
Improvement Factor ◽  
The One ◽  
Good Agreement

The one-dimensional, unsteady flow in an air-to-air heat exchanger is studied. The governing equations are derived and the method of characteristics with the uniform interval scheme is used in the analysis. The effect of the fin improvement factor on the air temperature in the heat exchanger and the heat transfer rate of the heat exchanger, and air properties in the heat exchanger are analyzed. The numerical results are compared and show good agreement with the available data.

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