Department Seminar: Anne Staples

Anne Staples, Ph.D., Assistant Professor, Department of Engineering Science and Mechanics at Virginia Tech University. Topic: "Turbulence and Human Physiology: Two Challenging Multiscale Problems." It has long been the standard approach in engineering and science to model the behavior of systems over a limited range of temporal and spatial scales. In general, we seek to derive closed, partial differential equations that govern phenomena in some small range of scales. When we are exceptionally lucky, we can model phenomena occurring on other scales in closed form. An example of this approach is the Navier-Stokes equations, in which the microscopic processes are represented by an equation of state and some linear constitutive relations. Most problems of interest in nature, however, involve a wide range of active scales, and the types of problems we are interested in solving now necessitate a new paradigm for solution methods in which we begin to consider systems with multi-scales and multi-physics on multi-grids. This presentation describes two very different problems. The first problem uses a heterogeneous computational multi-scale method (HMM) to speed up simulations of low-dimensional homogeneous turbulence models by taking advantage of the separation of time scales in the evolution of the energy spectrum. The second problem involves compiling a precise, consistent, and eventually comprehensive description of the human body as a complex network of multi-scale, multi-physics computational models of physiological systems and their couplings.

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