Robust Grid Adaptation for Efficient Uncertainty Quantification

Robust Grid Adaptation for Efficient Uncertainty Quantification

In the recent past, adjoint methods have been successfully applied in error estimation of integral outputs (functionals) of the numerical solution of partial differential equations. The adjoint solution can also be used as a grid adaptation indicator, with the objective of optimally targeting and reducing the numerical error in the functional of interest below a prespecified threshold. In situa...

Uncertainty Quantification for Robust Design

Simulation-based performance prediction has been an active research topic for many years and is now applied for industrial test-cases in all fields of computational mechanics. However, classical methods developed in Computational Fluid Dynamics (CFD) or Computational Structural Mechanics (CSM) usually assume a perfect knowledge of the parameters of the system studied, such as geometry, operatio...

Adaptation of Structured Grid for Supersonic and Transonic Flows

Two distinct redistribution grids - adaptation techniques, spring analogy and elliptic grid generator are applied to two-dimensional steady, inviscid, shocked flows, and the ability of each technique is examined and compared. Euler equations are solved base on Roe's Reimann solver approach to simulate supersonic flow around a sphere, transonic flow about an airfoil and supersonic flow in a symm...

An Efficient Computational Framework for Uncertainty Quantification in Multiscale Systems

Efficient Uncertainty Quantification with Polynomial Chaos for Implicit Stiff Systems

The polynomial chaos method has been widely adopted as a computationally feasible approach for uncertainty quantification. Most studies to date have focused on non-stiff systems. When stiff systems are considered, implicit numerical integration requires the solution of a nonlinear system of equations at every time step. Using the Galerkin approach, the size of the system state increases from n ...