Numerical simulation of high frequency waves in highly heterogeneous media is a challenging problem. Resolving the fine structure of the wave field typically requires extremely small time steps and spatial meshes. We show that capturing macroscopic quantities of the wave field, such as the wave energy density, is achievable with much coarser discretizations. We obtain such a result using a time splitting algorithm that solves separately and successively propagation and scattering in the simplified...
Numerical simulation of high frequency waves in highly heterogeneous
media is a challenging problem. Resolving the fine structure of the
wave field typically requires extremely small time steps and spatial
meshes. We show that capturing macroscopic quantities of the wave
field, such as the wave energy density, is achievable with much
coarser discretizations. We obtain such a result using a time
splitting algorithm that solves separately and successively
propagation and scattering in the...
A one-dimensional system describing the propagation of low Mach number flames in
sprays is studied. We show that pulsating waves may exist when the droplet distribution in the unburnt region is spatially periodic. The range of possible propagation speeds may be either bounded or unbounded, depending on the threshold temperatures of the burning and vaporization rates.
We extend, to parabolic equations of the KPP type in periodic media, a result of Bramson which asserts that, in the case of a spatially homogeneous reaction rate, the time lag between the position of an initially compactly supported solution and that of a traveling wave grows logarithmically in time.
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