Adaptive time-stepping for incompressible flow part I: scalar advection-diffusion

Even the simplest advection-diffusion problems can exhibit multiple time scales. This means that robust variable step time integrators are a prerequisite if such problems are to be efficiently solved computationally. The performance of the second order trapezoid rule using an explicit Adams–Bashforth method for error control is assessed in this work. This combination is particularly well suited to long time integration of advection-dominated problems. Herein it is shown that a stabilized implementation of the trapezoid rule leads to a very effective integrator in other situations: specifically diffusion problems with rough initial data; and general advection-diffusion problems with different physical time scales governing the system evolution

Adaptive time-stepping for incompressible flow. Part II: Navier-Stokes equations

We outline a new class of robust and efficient methods for solving the Navier- Stokes equations. We describe a general solution strategy that has two basic building blocks: an implicit time integrator using a stabilized trapezoid rule with an explicit Adams-Bashforth method for error control, and a robust Krylov subspace solver for the spatially discretized system. We present numerical experiments illustrating the potential of our approach. © 2010 Society for Industrial and Applied Mathematics

Goal driven optimization of process parameters for maximum efficiency in laser bending of advanced high strength steels

Laser forming or bending is fast becoming an attractive option for the forming of advanced high strength steels (AHSS), due primarily to the reduced formability of AHSS when compared with conventional steels in traditional contact-based forming processes. An inherently iterative process, laser forming must be optimized for efficiency in order to compete with contact based forming processes; as such, a robust and accurate method of optimal process parameter prediction is required. In this paper, goal driven optimization is conducted, utilizing numerical simulations as the basis for the prediction of optimal process parameters for the laser bending of DP 1000 steel. A key consideration of the optimization process is the requirement for minimal microstructural transformation in automotive grade high strength steels such as DP 1000