An epidemic disease caused by a new coronavirus has spread in Northern Italy with strong contagion rate. We implement an SEIR model to compute the infected population and number of casualties this epidemic. The example may ideally regard situation Italian Region Lombardy, where started on February 24, but no means attempts perform rigorous case study view lack suitable data uncertainty different parameters, namely, variation degree home isolation social distancing as function time, initial...

Low-order nonconforming Galerkin methods will be analyzed for second-order elliptic equations subjected to Robin, Dirichlet, or Neumann boundary conditions.Both simplicial and rectangular elements considered in two three dimensions.The based on P1, as conforming elements; however, it is necessary introduce new the case.Optimal order error estimates are demonstrated all cases with respect a broken norm H 1 (Ω) Robin L 2 (Ω).

Different theoretical and laboratory studies on the propagation of elastic waves in real rocks have shown that presence heterogeneities larger than pore size but smaller predominant wavelengths (mesoscopic-scale heterogeneities) may produce significant attenuation velocity dispersion effects seismic waves. Such phenomena are known as “mesoscopic effects” caused by equilibration wave-induced fluid pressure gradients. We propose a numerical upscaling procedure to obtain equivalent viscoelastic...

A theory to describe the propagation of elastic waves in a porous medium saturated by mixture two immiscible, viscous, compressible fluids is presented. First, using principle virtual complementary work, stress–strain relations are obtained for both anisotropic and isotropic media. Then forms kinetic dissipative energy density functions derived under assumption that relative flow within laminar type obeys Darcy’s law two-phase The equations motion derived, discussion different kinds body...

A method is presented to determine the elastic constants for an isotropic, porous, solid saturated by a two-phase fluid. Assuming that shear modulus of empty matrix known, it shown six additional coefficients in stress–strain relations can be uniquely determined performing two ideal experiments referred as ‘‘generalized jacketed and partially compressibility tests,’’ analogy with single-phase theory Biot. Under reasonable assumptions on behavior material, yield expressions terms material...

Abstract An epidemic disease caused by a new coronavirus has spread in Northern Italy with strong contagion rate. We implement an SEIR model to compute the infected population and number of casualties this epidemic. The example may ideally regard situation Italian Region Lombardy, where started on February 24, but no means attempts perform rigorous case study view lack suitable data uncertainty different parameters, namely, variation degree home isolation social distancing as function time,...

Using Biot’s theory to describe the propagation of elastic waves in a fluid-saturated porous solid (a Biot medium), reflection and transmission coefficients were computed at plane interface between fluid medium interfaces inside defined by either change saturant fluids or intrinsic rock permeability. The with without inclusion frequency correction factor that according has be introduced equations above certain critical (‘‘frequency-dependent’’ versus ‘‘classic model’’). For fluid–Biot range...

A naturally parallelizable numerical method for approximating scalar waves in a single space variable is developed by going to frequency domain formulation. General forms of attenuation are permitted. Convergence established and results presented.

Fractures are common in the Earth's crust due to different factors, for instance, tectonic stresses and natural or artificial hydraulic fracturing caused by a pressurized fluid. A dense set of fractures behaves as an effective long-wavelength anisotropic medium, leading azimuthally varying velocity attenuation seismic waves. Effective this case means that predominant wavelength is much longer than fracture spacing. Here, represented surface discontinuities displacement u particle v , where...

A dominant P-wave attenuation mechanism in reservoir rocks at seismic frequencies is due to wave-induced fluid flow (mesoscopic loss). The induces a fluid-pressure difference mesoscopic-scale inhomogeneities (larger than the pore size but smaller wavelength), generating and slow (diffusion) Biot waves. theory has been developed 1970s for symmetry axis of equivalent transversely isotropic (TI) medium corresponding finely layered medium, recently generalized all propagation angles. new states...

SUMMARY Thermoelastic attenuation is similar to wave-induced fluid-flow (mesoscopic loss) due conversion of the fast P wave slow (Biot) mode. In thermoelastic case, P- and S-wave energies are lost because thermal diffusion. The mode diffusive at low frequencies wave-like high frequencies, in same manner as Biot Therefore, that is, neglecting inertial terms, a mathematical analogy can be established between diffusion equations poroelasticity thermoelasticity. We study dissipation for...

A numerical method for approximating a pseudodifferential system describing attenuated, scalar waves is introduced and analyzed. Analytic properties of the solutions systems are determined used to show convergence method. Experiments using reported.

P-wave attenuation by slow-wave diffusion is a significant loss mechanism at seismic frequencies. This effect known as mesoscopic loss, because it consequence of fluid flow mesoscopic-scale inhomogeneities. These are larger than the pore size but smaller wavelength, typically tens centimeters, and due to local variations in lithological properties or patches immiscible fluids. Basically, traveling porous medium induces fluid-pressure gradient regions different properties, such saturated with...

A recent article [J. M. Carcione and G. Seriani, J. Comput. Phys. 170, 676 (2001)] proposes a modeling algorithm for wave simulation in three-phase porous medium composed of sand grains, ice, water. The differential equations hold uniform water (ice) content. Here, we obtain the variable-porosity by using analogy with two-phase case complementary energy theorem. displacements rock ice frames variation fluid content are generalized coordinates, stress components pressure forces. We simulate...

Finely layered media behaves as an anisotropic medium at long wavelengths. If the constituent are anelastic, Q ‐anisotropy of qP, qSV and SH waves can be described by a generalization Backus averaging to lossy case. To test theory, we introduce novel method obtain complex frequency‐dependent stiffnesses from numerical simulations oscillatory (harmonic) tests based on space‐frequency domain finite element method. We apply methodology periodic sequence shale limestone compute quality factor...

We develop a petro‐elastical numerical methodology to compute realistic synthetic seismograms and analyze the sensitivity of seismic response when injecting carbon dioxide (CO 2 ) in depleted gas reservoir. The model describes properties reservoir rock saturated with CO , methane brine, allows us estimate distribution saturation during injection process. properties, as function in‐situ pressure temperature conditions, are computed Peng‐Robinson equation state, taking into account absorption...