Multi space reduced basis preconditioners for parametrized Stokes equations

We introduce a two-level preconditioner for the efficient solution of large scale saddle-point linear systems arising from the finite element (FE) discretization of parametrized Stokes equations. This preconditioner extends the Multi Space Reduced Basis (MSRB) preconditioning method proposed in Dal Santo et al. (2018); it combines an approximated block (fine grid) preconditioner with a reduced basis (RB) solver which plays the role of coarse component. A sequence of RB spaces, constructed either with an enriched velocity formulation or a Petrov–Galerkin projection, is built. Each RB coarse component is defined to perform a single iteration of the iterative method at hand. The flexible GMRES (FGMRES) algorithm is employed to solve the resulting preconditioned system and targets small tolerances with a very small iteration count and in a very short time. Numerical test cases for Stokes flows in three dimensional parameter-dependent geometries are considered to assess the numerical properties of the proposed technique in different large scale computational settings.     

Implicit methods for viscous incompressible flows

Numerical methods and simulation tools for incompressible flows have been advanced largely as a subset of the computational fluid dynamics (CFD) discipline. Especially within the aerospace community, simulation of compressible flows has driven most of the development of computational algorithms and tools. This is due to the high level of accuracy desired for predicting aerodynamic performance of flight vehicles. Conversely, low-speed incompressible flow encountered in a wide range of fluid engineering problems has not typically required the same level of numerical accuracy. This practice of tolerating relatively low-fidelity solutions in engineering applications for incompressible flow has changed. As the design of flow devices becomes more sophisticated, a narrower margin of error is required. Accurate and robust CFD tools have become increasingly important in fluid engineering for incompressible and low-speed flow. Accuracy depends not only on numerical methods but also on flow physics and geometry modeling. For high-accuracy solutions, geometry modeling has to be very inclusive to capture the elliptic nature of incompressible flow resulting in large grid sizes. Therefore, in this article, implicit schemes or efficient time integration schemes for incompressible flow are reviewed from a CFD tool development point of view. Extension of the efficient solution procedures to arbitrary Mach number flows through a unified time-derivative preconditioning approach is also discussed. The unified implicit solution procedure is capable of solving low-speed compressible flows, transonic, as well as supersonic flows accurately and efficiently. Test cases demonstrating Mach-independent convergence are presented.     

Separation-bubble flow solution using Euler/Navier-Stokes zonal approach with downstream compatibility conditions

An Euler/Navier-Stokes zonal scheme is developed to numerically simulate the two-dimensional flow over a blunt leading-edge plate. The computational domain has been divided into inner and outer regions where the Navier-Stokes and Euler equations are used, respectively. On the downstream boundary, compatibility conditions derived from the boundary-layer equations are used. The grid is generated by using conformal mapping and the problem is solved by using a compressible Navier-Stokes code, which has been modified to treat Euler and Navier-Stokes regions. The accuracy of the solution is determined by the reattachment location. Bench-mark solutions have been obtained using the Navier-Stokes equations throughout the optimum computational domain and size. The problem is recalculated with sucessive decrease of the computational domain from the downstream side where the compatibility conditions are used, and with successive decrease of the Navier-Stokes computational region. The results of the zonal scheme are in excellent agreement with those of the benchmark solutions and the experimental data. The CPU time saving is about 15%.     

LU分解递归算法的实现

§1.引言 以LU分解, Cholesky分解等为代表的线性代数问题的数值计算在现代科学研究和工程技术中得到广泛应用.随着计算机技术的发展,实现这些线性代数数值计算的计算机算法和软件也在不断发展.目前,具有多级存储结构的高性能RISC计算机已占据了数值计算领域的主导地位. RSIC处理器的运算速度非常快,它们与存储器之间的速度差距很大.计算机的性能能不能充分发挥,多级存储结构与高缓能否得到有效利用成为关键.为此,现行的     

Automated adaptive cardiovascular flow simulations

We present an automatic adaptive procedure to perform blood flow simulations in the cardiovascular system. The procedure allows the user to start with subject-specific data collected through clinical measurements, like magnetic resonance imaging (MRI) data, and evaluate physiological parameters of interest, like flow distribution, pressure variations, wall shear stress, in an automatic and efficient manner. The process involves construction of geometric models of blood vessels, specification of flow conditions and application of an adaptive flow solver. The latter is based on incompressible Navier–Stokes equations using adaptive spatial discretization (meshing) techniques. In this article, we demonstrate the method on a model of a human abdominal aorta of a normal subject with geometry and flow rates assimilated from MRI data. The results obtained show that boundary layer mesh adaptivity offers a better alternative leading to more accurate predictions, especially for key physiological quantities like wall shear stress.     

Molecular dynamics-based unstructured grid generation method for aerodynamic applications

A new approach to triangular mesh generation based on the molecular dynamics method is proposed. Mesh nodes are considered as interacting particles. After the node placement by molecular dynamics simulation, well-shaped triangles or tetrahedra can be created after connecting the nodes by Delaunay triangulation or tetrahedrization. Some examples are considered in order to illustrate the method’s ability to generate a mesh for an aircraft with a complicated boundary. Mesh adaptation technology for molecular dynamics simulation is presented.     

Direct numerical simulation of turbulent flows with chemical reaction

Results from full turbulence simulations incorporating the effects of chemical reaction are compared with simple closure theories and used to reveal some physical insights about turbulent reacting flows. Pseudospectral methods for homogeneous turbulent flows with constant physical and thermal properties in domains as large as 64³ Fourier modes were used for these simulations. For the case of nonpremixed flows involving a two-species, second-order, irreversible chemical reaction, it is found that the scalar dissipation microscale is only a weak function of the reaction rate and that chemical reaction contributes very little to the decay of the variance of the reactant concentration. Examination of local values of the velocity and concentration fields shows that the local reaction rate is highest in regions of the greatest rates of strain and that vorticity tends to align with the reaction zone. Finally, difficulties associated with the evaluation of multipoint pdf's and with the archival of time-dependent data from the threedimensional simulations are described.Presented at the Second Nobeyama Workshop on Fluid Mechanics and Supercomputers, Nobeyama, Japan (September 1987).     

并行计算在弧形翼弹数值仿真中的应用

在以MPICH技术构建的局域网集群系统下,利用并行计算程序进行了超声速弧形翼-身组合体的三维绕流流场数值仿真,得到了弧形翼射弹的流场信息;并且通过对不同数量网格在集群不同结点数目下的计算结果进行分析比较,得出了加速比和并行效率随结点数目变化的规律,发现大规模网格在加速比和并行效率方面性能优越,更适合集群系统的并行计算,同时验证了此集群系统在数值仿真应用中的有效性和优越性,为进行大规模科学工程计算提供了技术支持.     

Computational flowfield analyses of hypersonic problems with reacting boundary layer

A mathematical model able to deal with high temperature gas effects in hypersonic flow fields is presented. In order to assess this model, four typical hypersonic applications are considered. The numerical results are presented and compared with experimental data. The effects of the catalyticity of the materials on the heat fluxes are also highlighted.     

Three-dimensional discrete-velocity BGK model for the incompressible Navier–Stokes equations

The lattice Boltzmann method (LBM) has been widely used for the simulations of the incompressible Navier–Stokes (NS) equations. The finite difference Boltzmann method (FDBM) in which the discrete-velocity Boltzmann equation is solved instead of the lattice Boltzmann equation has also been applied as an alternative method for simulating the incompressible flows. The particle velocities of the FDBM can be selected independently from the lattice configuration. In this paper, taking account of this advantage, we present the discrete velocity Boltzmann equation that has a minimum set of the particle velocities with the lattice Bharnagar–Gross–Krook (BGK) model for the three-dimensional incompressible NS equations. To recover incompressible NS equations, tensors of the particle velocities have to be isotropic up to the fifth rank. Thus, we propose to apply the icosahedral vectors that have 13 degrees of freedom to the particle velocity distributions. Validity of the proposed model (D3Q13BGK) is confirmed by numerical simulations of the shear-wave decay problem and the Taylor–Green vortex problem. With respect to numerical accuracy, computational efficiency and numerical stability, we compare the proposed model with the conventional lattice BGK models (D3Q15, D3Q19 and D3Q27) and the multiple-relaxation-time (MRT) model (D3Q13MRT) that has the same degrees of freedom as our proposal. The comparisons show that the compressibility error of the proposed model is approximately double that of the conventional lattice BGK models, but the computational efficiency of the proposed model is superior to that of the others. The linear stability of the proposed model is also superior to that of the lattice BGK models. However, in non-linear simulations, the proposed model tends to be less stable than the others.     

Numerical simulation of vortical flows in the near field of jets from notched circular nozzles

The vortex dominated flows in the near field of jets from notched circular nozzles are investigated using direct numerical simulation. The nozzles studied include a normal circular nozzle, a V-shaped notched nozzle, and an A-shaped notched nozzle, all with the same circular cross-section. The vortical structures resulting from these different circular nozzles are visualized by using a numerical dye visualization technique. Results for the V-shaped notched nozzle are compared with available experimental measurements using laser-induced fluorescence techniques. In addition to azimuthal vortex rings created because of the shear-layer between the jet and the ambient fluid, the computations also reveal streamwise vortex pairs both inside and outside the vortex rings that spread outward as the vortex rings move downstream. Comparisons of the three different nozzles show that, unlike in the case of the circular nozzle where the streamwise vortex pairs emerge evenly along the nozzle lip, streamwise vortex pairs for the notched circular nozzles are produced only at peak and trough locations. Analysis of the mixing characteristics of the three types of nozzles shows that the notches in the nozzle exit significantly enhance jet mixing.     

Sources of error in the graphical analysis of CFD results

Graphical techniques are widely used to analyze CFD solutions. Some of these techniques have inherent errors, making them represent the solution imprecisely. An understanding of these errors is important for proper interpretation of the computed results and for comparison with experiments. Examples include contouring, plotting of vector fields, particle tracing, and computation of flow functions involving integration or differentiation.This paper is declared a work of the U. S. Government and therefore is in the public domain.     

A DNS algorithm using B-spline collocation method for compressible turbulent channel flow

Direct numerical simulation (DNS) offers useful information about the understanding and modeling of turbulent flow. However, few DNSs of wall-bounded compressible turbulent flows have been performed. The objective of this paper is to construct a DNS algorithm which can simulate the compressible turbulent flow between the adiabatic and isothermal walls accurately and efficiently. Since this flow is the simplest turbulent flow with adiabatic and isothermal walls, it is ideal for the modeling of compressible turbulent flow near the adiabatic and isothermal walls. The present DNS algorithm for wall-bounded compressible turbulent flow is based on the B-spline collocation method in the wall-normal direction. In addition, the skew-symmetric form for convection term is used in the DNS algorithm to maintain numerical stability. The validity of the DNS algorithm is confirmed by comparing our results with those of an existing DNS of the compressible turbulent flow between isothermal walls [J. Fluid Mech. 305 (1995) 159]. The applicability and usefulness of the DNS algorithm are demonstrated by the stable computation of the DNS of compressible turbulent flow between adiabatic and isothermal walls.     

A three-dimensional model of primary thrombus formation based on fluid dynamics and level sets

In this paper, a three-dimensional (3D) multiscale model is proposed for the formation process of a primary thrombus. In the model, blood plasma is modelled by Navier–Stokes equations in macroscale because the blood plasma is seen as a continuous viscous fluid. The adhesion and aggregation of platelets are the main physiological processes of primary thrombus formation. As platelets and the primary thrombus are seen as rigid solids, these physiological processes are modelled in microscale according to the force related to the distance between the two solid bodies. We use level sets to represent the growth of the primary thrombus in 3D, and the multiscale model is applied to the 3D simulation of the primary thrombus formation. From numerical observations, the appearance of the formation process shows that it was affected by the change of blood-flow velocities. We can conclude that the appearance of the primary thrombus affects vascular blood flow.     

Three dimensional numerical simulations of long-span bridge aerodynamics, using block-iterative coupling and DES

The design of long-span bridges often depends on wind tunnel testing of sectional or full aeroelastic models. Some progress has been made to find a computational alternative to replace these physical tests. In this paper, an innovative computational fluid dynamics (CFD) method is presented, where the fluid-structure interaction (FSI) is solved through a self-developed code combined with an ANSYS-CFX solver. Then an improved CFD method based on block-iterative coupling is also proposed. This method can be readily used for two dimensional (2D) and three dimensional (3D) structure modelling. Detached-Eddy simulation for 3D viscous turbulent incompressible flow is applied to the 3D numerical analysis of bridge deck sections. Firstly, 2D numerical simulations of a thin airfoil demonstrate the accuracy of the present CFD method. Secondly, numerical simulations of a U-shape beam with both 2D and 3D modelling are conducted. The comparisons of aerodynamic force coefficients thus obtained with wind tunnel test results well meet the prediction that 3D CFD simulations are more accurate than 2D CFD simulations. Thirdly, 2D and 3D CFD simulations are performed for two generic bridge deck sections to produce their aerodynamic force coefficients and flutter derivatives. The computed values agree well with the available computational and wind tunnel test results. Once again, this demonstrates the accuracy of the proposed 3D CFD simulations. Finally, the 3D based wake flow vision is captured, which shows another advantage of 3D CFD simulations. All the simulation results demonstrate that the proposed 3D CFD method has good accuracy and significant benefits for aerodynamic analysis and computational FSI studies of long-span bridges and other slender structures.