New Math Solves Wave Problems in Oil, Medical Imaging Faster
Researchers have developed a faster computational method for simulating how waves travel through complex materials like rock and human tissue. The breakthrough could speed up seismic exploration for oil and gas, improve medical ultrasound devices, and reduce computing costs for industries that rely on wave simulations.
Originaltitel: Stable and high-order accurate finite difference methods for the diffusive viscous wave equation
<p>The diffusive viscous wave equation describes wave propagation in diffusive and viscous media. Examples include seismic waves traveling through the Earth's crust, taking into account of both the elastic properties of rocks and the dissipative effects due to internal friction and viscosity; acoustic waves propagating through biological tissues, where both elastic and viscous effects play a significant role. We propose a stable and high-order finite difference method for solving the governing equations. By designing the spatial discretization with the summation-by-parts property, we prove stability by deriving a discrete energy estimate. In addition, we derive error estimates for problems with constant coefficients using the normal mode analysis and for problems with variable coefficients using the energy method. Numerical examples are presented to demonstrate the stability and accuracy properties of the developed method.</p>