Showing papers by "Mark H. Carpenter published in 2007"
TL;DR: This work constructs a stable high-order finite difference scheme for the compressible Navier-Stokes equations, that satisfy an energy estimate, and shows the theoretical third-, fourth-, and fifth-order convergence rate, for a viscous shock, where the analytic solution is known.
281 citations
TL;DR: A discontinuous Galerkin finite element method (DGFEM) along with recently introduced high-order implicit-explicit Runge-Kutta (IMEX-RK) schemes to overcome geometry-induced stiffness in fluid-flow problems.
172 citations
TL;DR: Numerical computations of a more complex problem, a vortex-airfoil interaction, show that high-order methods are necessary to capture the significant flow features for transient problems and realistic grid resolutions.
67 citations
01 Apr 2007
TL;DR: In this article, a methodology for approximating realistic 3D fluid actuators, using quasi-1-D reduced-order models, is presented, at a fraction of the cost of full simulation and only a modest increase in cost relative to most actuator models used today.
Abstract: Accurate details of the general performance of fluid actuators is desirable over a range of flow conditions, within some predetermined error tolerance. Designers typically model actuators with different levels of fidelity depending on the acceptable level of error in each circumstance. Crude properties of the actuator (e.g., peak mass rate and frequency) may be sufficient for some designs, while detailed information is needed for other applications (e.g., multiple actuator interactions). This work attempts to address two primary objectives. The first objective is to develop a systematic methodology for approximating realistic 3-D fluid actuators, using quasi-1-D reduced-order models. Near full fidelity can be achieved with this approach at a fraction of the cost of full simulation and only a modest increase in cost relative to most actuator models used today. The second objective, which is a direct consequence of the first, is to determine the approximate magnitude of errors committed by actuator model approximations of various fidelities. This objective attempts to identify which model (ranging from simple orifice exit boundary conditions to full numerical simulations of the actuator) is appropriate for a given error tolerance.