Research in acoustics, combustion and fluid-structure interactions share a common theme of mathematical modeling and numerical simulation of problems in fluid and solid mechanics. Applications in these areas often involve wave propagation in complex constitutive materials, such as acoustic wave propagation in non-uniform media, detonation in heterogeneous explosives, or nonlinear deformation in elastic solids, among others. Mathematical models in these areas involve systems of partial differential equations, usually nonlinear and of hyperbolic type, together with matching conditions at interfaces in multi-material applications. For the latter applications, the dynamics of interfaces separating materials is an important feature of the problem, and developing stable and robust numerical tools for their accurate simulation is essential.

Researchers at Rensselaer are tackling interesting modeling issues related to long-range acoustic wave propagation in the ocean interacting with multicomponent sediments at the ocean floor, high-speed compressible flow in multiphase reactive materials, and compressible and incompressible fluids interacting with deformable structures, such as blood flow in veins and arties. A significant aspect of the active research concerns the development of numerical algorithms for the accurate solution of the model equations, and faculty in the math department are among the leaders in developing advanced simulation tools in these exciting areas of research.

Faculty Researchers:

• Jeffrey Banks
• Donald Schwendeman
• William Henshaw