Calculating magnetic fields around superconductors using conformal mappings

Superconductors expel magnetic fields, a phenomenon known as the Meissner effect. This effect makes it notoriously difficult to predict the magnetic field around a superconductor. One successful way of calculating these fields is through conformal mappings; coordinate transformations that preserve Maxwell's equations of magnetic fields in free...

Semi-analytical solution for the 3D response of a tunnel embedded in an elastic half-space subject to seismic waves

This paper presents a semi-analytical solution for the 3D problem of a cylindrical tunnel embedded in an elastic half-space subject to plane harmonic compressional and shear waves. Both the tunnel and soil are modelled as an elastic continuum. Conformal mapping is employed to transform the original physical domain with boundary surfaces of two...

Steady-State Flow Through a Subsurface Reservoir with a Displaced Fault and its Poro-elastic Effects on Fault Stresses

We consider steady-state single-phase confined flow through a subsurface porous layer containing a displaced, fully conductive fault causing a sudden jump in the flow path, and we employ (semi-)analytical techniques to compute the corresponding pressures and fault stresses. In particular, we obtain a new solution for the pressure field with...

Scattering of harmonic P1 and SV waves by a shallow lined circular tunnel in a poroelastic half-plane

An analytical solution for the scattering of harmonic P1 and SV waves in a poroelastic half-plane with a shallow lined tunnel is obtained using the plane complex theory in elastodynamics. In light of the wave function expansions, the wave fields of the poroelastic medium and the liner with unknown coefficients are obtained based on Biot's...

Semi-analytical solution for the dynamic response of a cylindrical structure embedded in a homogeneous half-space

This paper addresses the dynamic response of an infinitely long cylindrical structure embedded in an elastic half-space. The structure has a circular cross-section and its axis is parallel to the half-space surface. Excitation can be incident body waves or forces applied on the surface of the half-space and/or the structure. The model can be...

Visualization of space competition and plume formation with complex potentials for multiple source flows: Some examples and novel application to Chao lava flow (Chile)

Fluid displacement in a continuum pressured by a variable constellation of source flows can be visualized as solutions of line integrals. The algorithms are based on complex potentials that provide exact solutions of the Navier-Stokes equation and allow users to specify both the location and flux strength of multiple sources. If relative...

Conformal mapping potential flow around a wingsection used as a test case for the inviscid part of RANS solvers

The Theodorsen-Garrick conformal mapping is used to make a grid around a wing section and to compute the potential flow around it. The potential flow is a solution to the incompressible Euler equations and can be used to verify the inviscid part of RANS codes.