Anisotropic Mesh Refinement for Discontinuous Galerkin Methods in Aerodynamic Flow Simulations

Two types of anisotropic indicators are derived which can be used within an anisotropic refinement algorithm for 2nd but also for higher order Discontinuous Galerkin discretizations. Whereas the first type of indicator employs the possible interelement discontinuities of the discrete functions the second type of indicator estimates the approximation error in terms of 2nd but possibly also higher order derivatives. A simple extension of these indicators to systems of equations is implemented which performs better than the so-called metric intersection used to combine the metric information of several solution components. The anisotropic indicators are incorporated into an adaptive refinement algorithm which uses state-of-the-art residual-based or adjoint-based indicators for goal-oriented refinement to select the elements to be refined whereas the anisotropic indicators determine which anisotropic case the selected elements shall be refined with. The performance of the anisotropic refinement algorithm is demonstrated for sub-, trans- and supersonic, inviscid and viscous compressible flows around the NACA0012 airfoil

Steady-state Flow Solutions for Delta Wing Configurations at High Angle of Attack using Implicit Schemes

Finding fully converged, steady-state solutions of the compressible Reynolds Averaged Navier-Stokes (RANS) equations for aerodynamic configurations on the border of the flight envelope often poses serious challenges to solution algorithms that have proven robust and successful for configurations at cruise conditions. Examples of such cases are agile configurations at high angles of attack. When trying to compute solutions in these scenarios, one often observes that the solution process breaks down after few iterations or that a steady-state RANS solution, although it may exist, cannot be reached with the employed solution algorithm. While, in general, no clear reason for this behavior can be identified, the complexity of these flows seems to be significantly greater compared to flows around transport aircraft in cruise flight. The flow fields are dominated by the interaction of shock waves with a system of vortices emanating from the leading edges on the upper surface of the wing, leading to massive flow separation. These flow features tend to be inherently unsteady and can be assumed to cause problems in computing a converged solution using an algorithm designed to find steady-state solutions of the RANS equations. To avoid these problems, it is not uncommon to calculate such configurations in an unsteady mode, which often comes at a rather high computational cost. This article demonstrates the necessity for implicit smoothers to approximate fully converged solutions of these challenging simulations. A numerical example is given to confirm that convergence is only possible using an exact derivative together with a suited preconditioner

A Machine Learning based Expert System for Optimizing CFD Solver Parameters

Computational Fluid Dynamics is a viable tool in the field of aerodynamics enabling to reduce time, effort and budget required for experimental testing. Although powerful and established for various years, it remains a complex tool calling for experienced users to ensure consistent high-quality results. This complexity primarily stems from the underlying model, namely the Navier-Stokes equations typically combined with a set of equations resolving the effects of turbulence. Additionally, to obtain accurate high-fidelity result appropriate meshes are required. As a consequence, a substantial number of parameters needs to be selected carefully and the quality of a result often highly depends on individual knowledge and experience of a user. Hence, a strong desire exists to reduce the number of input parameters without causing a loss of accuracy and efficiency. Such reduction of parameters might be viewed as a prerequisite to CFD as a tool in process chains for multidisciplinary applications where typically no user interaction is possible. In this article we propose a machine-learned Expert System for CFD to provide guidance for users in selecting optimal or at least near optimal parameter combinations. The proposed Expert System is divided into two macro steps, the surrogate model and a genetic algorithm to determine from the surrogate model the parameters. Numerical examples are presented to demonstrate the approach

Peptide Immunization Indicates that CD8+ T Cells are the Dominant Effector Cells in Trinitrophenyl-Specific Contact Hypersensitivity

The identity of the effector T cell population involved in contact hypersensitivity is still questionable with evidence promoting both CD4+ or CD8+ T cells. Previous experimental studies have relied on the in vivo depletion of T cell subsets using antibody, or the use of knock-out mice with deficiencies in either CD4+ or CD8+ T cell-mediated immunity. To address the role of the class I- and class II-mediated pathways of T cell activation in contact hypersensitivity responses in mice with an intact immune system, we utilized various trinitrophenyl-derivatized peptides, which bind specifically with H-2Kb (major histocompatibility complex class I) or H-2I-Ab (major histocompatibility complex class II). The subcutaneous injection of major histocompatibility complex class II-specific, but not of class I-binding, hapten-derivatized peptides in incomplete Freund's adjuvant induced specific, albeit low, contact hypersensitivity responsiveness to trinitrochlorobenzene. When bone-marrow-derived dendritic cells, however, were pulsed with the same peptides and administered intradermally, the opposite result was observed, namely that the class I binding peptides induced contact hypersensitivity responses similar to that observed after epicutaneous trinitrochlorobenzene application. In contrast, dendritic cells pulsed with major histocompatibility complex class II binding peptides did not reproducibly sensitize for contact hypersensitivity responses. Surprisingly, both immunization protocols efficiently induced CD8+ effector T cells. These results support the notion that CD8+ T cells are the dominant effector population mediating contact hypersensitivity responsiveness and that the CD4+ T cell subset only contributes little if at all

Simvastatin add-on to escitalopram in patients with comorbid obesity and major depression (SIMCODE): study protocol of a multicentre, randomised, double-blind, placebo-controlled trial

Introduction: Major depressive disorder (MDD) and obesity are both common disorders associated with significant burden of disease worldwide. Importantly, MDD and obesity often co-occur, with each disorder increasing the risk for developing the other by about 50%-60%. Statins are among the most prescribed medications with well-established safety and efficacy. Statins are recommended in primary prevention of cardiovascular disease, which has been linked to both MDD and obesity. Moreover, statins are promising candidates to treat MDD because a meta-analysis of pilot randomised controlled trials has found antidepressive effects of statins as adjunct therapy to antidepressants. However, no study so far has tested the antidepressive potential of statins in patients with MDD and comorbid obesity. Importantly, this is a difficult-to-treat population that often exhibits a chronic course of MDD and is more likely to be treatment resistant. Thus, in this confirmatory randomised controlled trial, we will determine whether add-on simvastatin to standard antidepressant medication with escitalopram is more efficacious than add-on placebo over 12 weeks in 160 patients with MDD and comorbid obesity. Methods and analysis: This is a protocol for a randomised, placebo-controlled, double-blind multicentre trial with parallel-group design (phase II). One hundred and sixty patients with MDD and comorbid obesity will be randomised 1:1 to simvastatin or placebo as add-on to standard antidepressant medication with escitalopram. The primary outcome is change in the Montgomery-angstrom sberg Depression Rating Scale (MADRS) score from baseline to week 12. Secondary outcomes include MADRS response (defined as 50% MADRS score reduction from baseline), MADRS remission (defined as MADRS score <10), mean change in patients' self-reported Beck Depression Inventory (BDI-II) and mean change in high-density lipoprotein, low-density lipoprotein and total cholesterol from baseline to week 12. Ethics and dissemination: This protocol has been approved by the ethics committee of the federal state of Berlin (Ethik-Kommission des Landes Berlin, reference: 19/0226-EK 11) and by the relevant federal authority (Bundesinstitut fur Arzneimittel und Medizinprodukte (BfArM), reference: 4043387). Study findings will be published in peer-reviewed journals and will be presented at (inter)national conferences

Investigation on Adjoint Based Gradient Computations for Realistic 3d Aero-Optimization

A discrete adjoint method for e�ciently computing gradients for aerodynamic shape op- timizations is presented. The chain itself involves an unstructured mesh Reynolds-Averaged Navier-Stokes solver, and is suitable for the optimization of complex geometries in three dimensions. In addition to the discrete ow adjoint the method introduces a second ad- joint equation for the mesh deformation. Using the adjoint chain it is possible to evaluate the gradients of a cost function for the cost of one adjoint ow solution and one adjoint volume mesh deformation, without performing any (forward) mesh deformation. By choos- ing a suitable mesh deformation operator, like linear elasticity, the chain may be readily constructed by hand. Furthermore, this adjoint chain can be subsequently used with pa- rameterized surface grids. The accuracy and the computational savings of the resulting procedure is examined for the gradient-based shape optimization of a wing in inviscid ow

Adjoint-based error estimation and adaptive mesh refinement for the RANS and k-ω turbulence model equations

In this article we present the extension of the a posteriori error estimation and goal-oriented mesh refinement approach from laminar to turbulent flows, which are governed by the Reynolds-averaged Navier-Stokes and k-ω turbulence model (RANS-kω) equations. In particular, we consider a discontinuous Galerkin discretization of the RANS-kω equations and use it within an adjoint-based error estimation and adaptive mesh refinement algorithm that targets the reduction of the discretization error in single as well as in multiple aerodynamic force coefficients. The accuracy of the error estimation and the performance of the goal-oriented mesh refinement algorithm is demonstrated for various test cases, including a two-dimensional turbulent flow around a three-element high lift configuration and a three-dimensional turbulent flow around a wing-body configuration

Error estimation and anisotropic mesh refinement for 3d laminar aerodynamic flow simulations

This article considers a posteriori error estimation and anisotropic mesh refinement for three-dimensional aerodynamic flow simulations. The optimal order symmetric interior penalty discontinuous Galerkin discretization which has previously been developed for the compressible Navier-Stokes equations in two dimensions is extended to three dimensions. Symmetry boundary conditions are given which allow to discretize and compute symmetric flows on the half model resulting in exactly the same flow solutions as if computed on the full model. Using duality arguments, an error estimation is derived for estimating the discretization error with respect to the aerodynamic force coefficients. Furthermore, residual-based indicators as well as adjoint-based indicators for goal-oriented refinement are derived. These refinement indicators are combined with anisotropic indicators which are particularly suited to the discontinuous Galerkin (DG) discretization. The performance of the proposed discretization, error estimation and adaptive mesh refinement algorithms is demonstrated for 3d aerodynamic flows