Review of Output-Based Error Estimation and Mesh Adaptation in Computational Fluid Dynamics

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/90641/1/AIAA-53965-537.pd

Goal-oriented error estimation for fluid-structure interaction problems

In this work, we present an adaptive finite element method for the numerical simulation of stationary fluid-structure interaction problems. The coupled system is given in a variational and monolithic Arbitrary Lagrangian Eulerian framework. We derive methods for goal-oriented error estimation and mesh adaptation with the dual weighted residual method. Key to applying this error estimator is the underlying canonic variational formulation of the fluid-structure interaction problem by mapping the flow problem to ALE coordinates. The developed method is applied to two and three dimensional stationary benchmark problems coupling the incompressible Navier-Stokes equations with a nonlinear hyper-elastic material law

Comparison of Mesh Adaptation Using the Adjoint Methodology and Truncation Error Estimates

Mesh adaptation based on error estimation has become a key technique to improve th eaccuracy o fcomputational-fluid-dynamics computations. The adjoint-based approach for error estimation is one of the most promising techniques for computational-fluid-dynamics applications. Nevertheless, the level of implementation of this technique in the aeronautical industrial environment is still low because it is a computationally expensive method. In the present investigation, a new mesh refinement method based on estimation of truncation error is presented in the context of finite-volume discretization. The estimation method uses auxiliary coarser meshes to estimate the local truncation error, which can be used for driving an adaptation algorithm. The method is demonstrated in the context of two-dimensional NACA0012 and three-dimensional ONERA M6 wing inviscid flows, and the results are compared against the adjoint-based approach and physical sensors based on features of the flow field

Adjoint-Based Error Estimation and Mesh Adaptation for Problems with Output Constraints

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/140439/1/6.2014-2576.pd

Unstructured Grid Adaptation: Status, Potential Impacts, and Recommended Investments Towards CFD 2030

International audienceUnstructured grid adaptation is a powerful tool to control Computational Fluid Dynamics (CFD) discretization error. It has enabled key increases in the accuracy, automation, and capacity of some fluid simulation applications. Slotnick et al. provide a number of case studies in the CFD Vision 2030 Study: A Path to Revolutionary Computational Aerosciences to illustrate the current state of CFD capability and capacity. The study authors forecast the potential impact of emerging High Performance Computing (HPC) environments forecast in the year 2030 and identify that mesh generation and adaptivity will continue to be significant bottlenecks in the CFD workflow. These bottlenecks may persist because very little government investment has been targeted in these areas. To motivate investment, the impacts of improved grid adaptation technologies are identified. The CFD Vision 2030 Study roadmap and anticipated capabilities in complementary disciplines are quoted to provide context for the progress made in grid adaptation in the past fifteen years, current status, and a forecast for the next fifteen years with recommended investments. These investments are specific to mesh adaptation and impact other aspects of the CFD process. Finally, a strategy is identified to di↵use grid adaptation technology into production CFD work flows

Goal-oriented a posteriori error estimation for the travel time functional in porous media flows

In this article we consider the a posteriori error estimation and adaptive mesh refinement for the numerical approximation of the travel time functional arising in porous media flows. The key application of this work is in the safety assessment of radioactive waste facilities; in this setting, the travel time functional measures the time taken for a non-sorbing radioactive solute, transported by groundwater, to travel from a potential site deep underground to the biosphere. To ensure the computability of the travel time functional, we employ a mixed formulation of Darcy's law and conservation of mass, together with Raviart-Thomas H(div) conforming finite elements. The proposed a posteriori error bound is derived based on a variant of the standard Dual-Weighted-Residual approximation, which takes into account the lack of smoothness of the underlying functional of interest. The proposed adaptive refinement strategy is tested on both a simple academic test case and a problem based on the geological units found at the Sellafield site in the UK

Multigoal-oriented a posteriori error control for heated material processing using a generalized Boussinesq model

In this work, we develop a posteriori error control for a generalized Boussinesq model in which thermal conductivity and viscosity are temperature-dependent. Therein, the stationary Navier–Stokes equations are coupled with a stationary heat equation. The coupled problem is modeled and solved in a monolithic fashion. The focus is on multigoal-oriented error estimation with the dual-weighted residual method in which an adjoint problem is utilized to obtain sensitivity measures with respect to several goal functionals. The error localization is achieved with the help of a partition-of-unity in a weak formulation, which is specifically convenient for coupled problems as we have at hand. The error indicators are used to employ adaptive algorithms, which are substantiated with several numerical tests such as one benchmark and two further experiments that are motivated from laser material processing. Therein, error reductions and effectivity indices are consulted to establish the robustness and efficiency of our framework