A Different Approach to Boundary Modelling for Neumann Condition on a Curved Boundary at Arbitrary Irregular Grids

2009 ◽  
Author(s):  
M. Arad ◽  
G. Ben-Dor ◽  
A. Yakhot
Keyword(s):  
Neumann Condition ◽  
Curved Boundary ◽  
Irregular Grids

scholarly journals Analytical solution for torsion of cylindrical orthotropic annular wedge-shaped bars reinforced by thin shells

2021 ◽  
Author(s):  
István Ecsedi ◽  
Attila Baksa
Keyword(s):  
Analytical Solution ◽  
Cross Section ◽  
Analytical Method ◽  
Torsional Rigidity ◽  
Circular Ring ◽  
Thin Shells ◽  
Elastic Wedge ◽  
Curved Boundary ◽  
Cylindrically Orthotropic ◽  
Boundary Surfaces

AbstractThis paper deals with the Saint-Venant torsion of elastic, cylindrically orthotropic bar whose cross section is a sector of a circular ring shaped bar. The cylindrically orthotropic homogeneous elastic wedge-shaped bar strengthened by on its curved boundary surfaces by thin isotropic elastic shells. An analytical method is presented to obtain the Prandtl’s stress function, torsion function, torsional rigidity and shearing stresses. A numerical example illustrates the application of the developed analytical method.

Time of first entry into a region with curved boundary

1979 ◽  
Vol 19 (4) ◽  
pp. 582-595 ◽  
Author(s):  
A. A. Mogul'skii ◽  
E. A. Pecherskii
Keyword(s):  
Curved Boundary

scholarly journals A Two-Scale Computational Model of pH-Sensitive Expansive Porous Media

2013 ◽  
Vol 80 (2) ◽  
Author(s):  
Ranena V. Ponce F. ◽  
Márcio A. Murad ◽  
Sidarta A. Lima
Keyword(s):  
Electrolyte Solution ◽  
Solid Phase ◽  
Scale Model ◽  
Bulk Solution ◽  
Neumann Condition ◽  
Pore Scale ◽  
Exchange Reactions ◽  
Layer Potential ◽  
Bulk Fluid ◽  
Monovalent Ions

We propose a new two-scale model to compute the swelling pressure in colloidal systems with microstructure sensitive to pH changes from an outer bulk fluid in thermodynamic equilibrium with the electrolyte solution in the nanopores. The model is based on establishing the microscopic pore scale governing equations for a biphasic porous medium composed of surface charged macromolecules saturated by the aqueous electrolyte solution containing four monovalent ions (Na+,Cl-,H+,OH-). Ion exchange reactions occur at the surface of the particles leading to a pH-dependent surface charge density, giving rise to a nonlinear Neumann condition for the Poisson–Boltzmann problem for the electric double layer potential. The homogenization procedure, based on formal matched asymptotic expansions, is applied to up-scale the pore-scale model to the macroscale. Modified forms of Terzaghi's effective stress principle and mass balance of the solid phase, including a disjoining stress tensor and electrochemical compressibility, are rigorously derived from the upscaling procedure. New constitutive laws are constructed for these quantities incorporating the pH-dependency. The two-scale model is discretized by the finite element method and applied to numerically simulate a free swelling experiment induced by chemical stimulation of the external bulk solution.

Dynamics of a Water Droplet over a Sessile Oil Droplet: Compound Droplets Satisfying a Neumann Condition

Langmuir ◽  
2017 ◽  
Vol 33 (23) ◽  
pp. 5713-5723 ◽  
Author(s):  
R. Iqbal ◽  
S. Dhiman ◽  
A. K. Sen ◽  
Amy Q. Shen
Keyword(s):  
Water Droplet ◽  
Neumann Condition ◽  
Oil Droplet

Topological sensitivity analysis revisited for time-harmonic wave scattering problems. Part I: the free space case

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Frédérique Le Louër ◽  
María-Luisa Rapún
Keyword(s):  
Free Space ◽  
Order Term ◽  
Harmonic Wave ◽  
Dirichlet Condition ◽  
Point Sources ◽  
Neumann Condition ◽  
Scattering Problems ◽  
Content Type ◽  
Time Harmonic ◽  
Topological Gradient

PurposeIn this paper, the authors revisit the computation of closed-form expressions of the topological indicator function for a one step imaging algorithm of two- and three-dimensional sound-soft (Dirichlet condition), sound-hard (Neumann condition) and isotropic inclusions (transmission conditions) in the free space.Design/methodology/approachFrom the addition theorem for translated harmonics, explicit expressions of the scattered waves by infinitesimal circular (and spherical) holes subject to an incident plane wave or a compactly supported distribution of point sources are available. Then the authors derive the first-order term in the asymptotic expansion of the Dirichlet and Neumann traces and their surface derivatives on the boundary of the singular medium perturbation.FindingsAs the shape gradient of shape functionals are expressed in terms of boundary integrals involving the boundary traces of the state and the associated adjoint field, then the topological gradient formulae follow readily.Originality/valueThe authors exhibit singular perturbation asymptotics that can be reused in the derivation of the topological gradient function that generates initial guesses in the iterated numerical solution of any shape optimization problem or imaging problems relying on time-harmonic acoustic wave propagation.

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