Two dimensional Riemann-type problem and shock diffraction for the Chaplygin gas

2020 ◽  
Vol 101 ◽  
pp. 106046
Author(s):  
Qin Wang ◽  
Jingqin Zhang ◽  
Hanchun Yang
Keyword(s):  
Chaplygin Gas ◽  
Two Dimensional ◽  
Type Problem ◽  
Shock Diffraction

Expansions with Poisson kernels and related topics

2010 ◽  
Vol 53 (1) ◽  
pp. 153-173 ◽  
Author(s):  
Cristina Giannotti ◽  
Paolo Manselli
Keyword(s):  
Unit Disc ◽  
Poisson Kernel ◽  
Cauchy Type ◽  
Two Dimensional ◽  
Type Problem ◽  
Special Sequence ◽  
Poisson Kernels ◽  
Cauchy Type Problem ◽  
In Series

AbstractLet P(r, θ) be the two-dimensional Poisson kernel in the unit disc D. It is proved that there exists a special sequence {ak} of points of D which is non-tangentially dense for ∂D and such that any function on ∂D can be expanded in series of P(|ak|, (·)–arg ak) with coefficients depending continuously on f in various classes of functions. The result is used to solve a Cauchy-type problem for Δu = μ, where μ is a measure supported on {ak}.

scholarly journals Function-based block multigrid strategy for a two-dimensional linear elasticity-type problem

2017 ◽  
Vol 74 (5) ◽  
pp. 1015-1028 ◽  
Author(s):  
Marco Donatelli ◽  
Ali Dorostkar ◽  
Mariarosa Mazza ◽  
Maya Neytcheva ◽  
Stefano Serra-Capizzano
Keyword(s):  
Linear Elasticity ◽  
Two Dimensional ◽  
Type Problem

Piston Problems of Two-Dimensional Chaplygin Gas

2019 ◽  
Vol 40 (6) ◽  
pp. 843-868 ◽  
Author(s):  
Shuxing Chen ◽  
Aifang Qu
Keyword(s):  
Chaplygin Gas ◽  
Two Dimensional

Poromechanics Solutions to Plane Strain and Axisymmetric Mandel-Type Problems in Dual-Porosity and Dual-Permeability Medium

2009 ◽  
Vol 77 (1) ◽  
Author(s):  
Vinh X. Nguyen ◽  
Younane N. Abousleiman
Keyword(s):  
Plane Strain ◽  
Laboratory Testing ◽  
Time Dependent ◽  
Polar Coordinates ◽  
Dual Porosity ◽  
External Loading ◽  
Two Dimensional ◽  
Loading Conditions ◽  
Type Problem ◽  
Secondary Porosity

The two-dimensional Mandel-type problem geometry is well-known to bio-geomechanicians for testing rocks, cartilages, and bones with solutions in Cartesian coordinates for rectangular specimens or polar coordinates for cylindrical and disk samples. To date, all existing solutions are only applicable to single-porosity and single-permeability models, which could fall short when the porous material exhibits multiporosity and/or multipermeability characteristics, such as secondary porosity or fracture. This paper extends the plane strain and axisymmetric Mandel-type solutions from single-to dual-porosity and dual-permeability poromechanics. The solutions are presented in explicit analytical forms and account for arbitrary time-dependent external loading conditions, e.g., cyclic and ramping. The derived analytical solutions and results exhibit general behaviors characterized by two time scales. Stresses, pore pressures, and displacements are plotted for various time scale ratios to illustrate the interplaying effects of permeability and stiffness contrast of both porous regions, in addition to the interporosity exchange, on the overall responses of the system. Also, examples with realistic loading conditions for laboratory testing or field simulation such as cyclic and ramping are provided to demonstrate the engineering applications of the presented dual-poroelastic formulation and solutions.

Two-Dimensional Riemann Problems for Chaplygin Gas

2012 ◽  
Vol 44 (3) ◽  
pp. 2146-2178 ◽  
Author(s):  
Shuxing Chen ◽  
Aifang Qu
Keyword(s):  
Chaplygin Gas ◽  
Two Dimensional ◽  
Riemann Problems
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