Micro-combustion modelling with RBF-FD: A high-order meshfree method for reactive flows in complex geometries

2021 ◽  
Vol 94 ◽  
pp. 635-655
Author(s):  
Víctor Bayona ◽  
Mario Sánchez-Sanz ◽  
Eduardo Fernández-Tarrazo ◽  
Manuel Kindelan
Keyword(s):  
Meshfree Method ◽  
High Order ◽  
Complex Geometries ◽  
Reactive Flows ◽  
Combustion Modelling

LOW AND HIGH ORDER FINITE ELEMENT METHOD: EXPERIENCE IN SEISMIC MODELING

1994 ◽  
Vol 02 (04) ◽  
pp. 371-422 ◽  
Author(s):  
E. PADOVANI ◽  
E. PRIOLO ◽  
G. SERIANI
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Computational Efficiency ◽  
High Order ◽  
Cholesky Factorization ◽  
Complex Geometries ◽  
Spectral Elements ◽  
Seismic Modeling ◽  
Static Condensation ◽  
Element Method

The finite element method (FEM) is a numerical technique well suited to solving problems of elastic wave propagation in complex geometries and heterogeneous media. The main advantages are that very irregular grids can be used, free surface boundary conditions can be easily taken into account, a good reconstruction is possible of irregular surface topography, and complex geometries, such as curved, dipping and rough interfaces, intrusions, cusps, and holes can be defined. The main drawbacks of the classical approach are the need for a large amount of memory, low computational efficiency, and the possible appearance of spurious effects. In this paper we describe some experience in improving the computational efficiency of a finite element code based on a global approach, and used for seismic modeling in geophysical oil exploration. Results from the use of different methods and models run on a mini-superworkstation APOLLO DN10000 are reported and compared. With Chebyshev spectral elements, great accuracy can be reached with almost no numerical artifacts. Static condensation of the spectral element's internal nodes dramatically reduces memory requirements and CPU time. Time integration performed with the classical implicit Newmark scheme is very accurate but not very efficient. Due to the high sparsity of the matrices, the use of compressed storage is shown to greatly reduce not only memory requirements but also computing time. The operation which most affects the performance is the matrix-by-vector product; an effective programming of this subroutine for the storage technique used is decisive. The conjugate gradient method preconditioned by incomplete Cholesky factorization provides, in general, a good compromise between efficiency and memory requirements. Spectral elements greatly increase its efficiency, since the number of iterations is reduced. The most efficient and accurate method is a hybrid iterative-direct solution of the linear system arising from the static condensation of high order elements. The size of 2D models that can be handled in a reasonable time on this kind of computer is nowadays hardly sufficient, and significant 3D modeling is completely unfeasible. However the introduction of new FEM algorithms coupled with the use of new computer architectures is encouraging for the future.

Large Eddy Simulations for 3D Turbine Blades Using a High Order Flux Reconstruction Method

2013 ◽  
Author(s):  
Yi Lu ◽  
Kai Liu ◽  
W. N. Dawes
Keyword(s):  
Turbine Blade ◽  
High Order ◽  
Large Eddy Simulations ◽  
Complex Geometries ◽  
Flux Reconstruction ◽  
Reconstruction Method ◽  
Order Accuracy ◽  
Local Reconstruction ◽  
Low Pressure Turbine ◽  
Large Eddy

During the last decades, the improvements of both computational ability and numerical schemes have stimulated increasing industrial interest in the use of Large Eddy Simulations (LES) for practical engineering flow problems. However, almost all current approches cannot treat complex geometries at affordable cost to enable LES of industrial problems. A robust, parallel and efficient solver using a general unstructured grid & based on high order flux reconstruction formulation, which uses local reconstruction, is compact and written in differential form without a mass matrix, was developed and has proved the ability to get accurate LES results but using RANS scale meshes. This work is aimed at using flux reconstruction method to perform Large Eddy Simulations for complex geometries in more robust and highly efficient way. Both explicit Runge-Kutta method and implicit LU-SGS method are implemented with improvements as solvers for better performance on boundary layer meshes including large aspect ratio cells. The current solver is ported to GPU architectures and speed up ratios of different order accuracy are presented in this work. A local reconstruction method is introduced to generate high order curved boundary from readily available first order meshes. The large eddy simulations for low pressure turbine blade and low pressure turbine blade with endwall are presented in this work, resolved with total number of degree of freedoms up to 34 million to chieve fourth order accuracy using limited computational resource. The results show that this approach has the potential to obtain LES results of real-geometry problems with affordable computational costs.

Higher Order Computations of the Convection-Diffusion Equation With Curved Boundaries

2003 ◽  
Author(s):  
Heejin Lee ◽  
Michael M. Chen
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
High Order ◽  
Complex Geometries ◽  
Third Order ◽  
Order Accuracy ◽  
Curved Boundaries ◽  
Structured Grid ◽  
The Finite Difference Method

In computational heat transfer and fluid mechanics, high order accuracy methods are desirable in order to reduce computational effort or to obtain more accurate solutions for a given mesh coarseness. On structured grids, the finite difference method is especially easy for deriving and implementing higher order schemes. In spite of this advantage, for complex geometries high order schemes have not been attractive due to the restriction of the structured grid in dealing with curved boundaries. Therefore, for complex geometries most computational methods are based on finite element or finite volume methods with unstructured or boundary-fitted mesh at the expense of difficult and complicated implementation. For this reason, few computations for complex geometries have attempted more than near-second-order accuracy. In our paper, we demonstrate a high order scheme to deal with curved boundaries of complex geometries in Cartesian coordinate system using the finite difference method, taking advantages of the ease and simplicity of structured grid. The method is based on an extension of the full second order methods presented previously by Jung et al. [2000] and Lee and Chen [2002]. The temperature distributions and maximum errors in a cylindrical solid and an annulus where the velocity distribution is given were calculated with a third order accurate scheme, and compared with exact solutions. Theoretical derivations and numerical experiments show that true third order accuracy have been attained in advection-diffusion problems with curved boundaries. The results reinforce the assertion that the same concepts can be extended to any order accuracy so far as such accuracy is deemed desirable for the problem of interest.

A parallel high-order compressible flows solver with domain decomposition method in the generalized curvilinear coordinates system

2019 ◽  
Vol 30 (1) ◽  
pp. 2-38 ◽  
Author(s):  
Arthur Piquet ◽  
Boubakr Zebiri ◽  
Abdellah Hadjadj ◽  
Mostafa Safdari Shadloo
Keyword(s):  
Domain Decomposition ◽  
Decomposition Method ◽  
Compressible Flows ◽  
Domain Decomposition Method ◽  
High Order ◽  
Curvilinear Coordinates ◽  
Compressible Turbulence ◽  
Complex Geometries ◽  
Content Type ◽  
Pipe Flows

Purpose This paper aims to present the development of a highly parallel finite-difference computational fluid dynamics code in generalized curvilinear coordinates system. The objectives are to handle internal and external flows in fairly complex geometries including shock waves, compressible turbulence and heat transfer. Design/methodology/approach The code is equipped with high-order discretization schemes to improve the computational accuracy of the solution algorithm. Besides, a new method to deal with the geometrical singularities, so-called domain decomposition method (DDM), is implemented. The DDM consists of using two different meshes communicating with each other, where the base mesh is Cartesian and the overlapped one a hollow cylinder. Findings The robustness of the present implemented code is appraised through several numerical test cases including a vortex advection, supersonic compressible flow over a cylinder, Poiseuille flow, turbulent channel and pipe flows. The results obtained here are in an excellent agreement when compared to the experimental data and the previous direct numerical simulation (DNS). As for the DDM strategy, it was successful as simulation time is clearly decreased and the connection between the two subdomains does not create spurious oscillations. Originality/value In sum, the developed solver was capable of solving, accurately and with high-precision, two- and three-dimensional compressible flows including fairly complex geometries. It is noted that the data provided by the DNS of supersonic pipe flows are not abundant in the literature and therefore will be available online for the community.

scholarly journals High Order Finite Difference Methods with Subcell Resolution for Stiff Multispecies Discontinuity Capturing

2015 ◽  
Vol 17 (2) ◽  
pp. 317-336 ◽  
Author(s):  
Wei Wang ◽  
Chi-Wang Shu ◽  
H.C. Yee ◽  
Dmitry V. Kotov ◽  
Björn Sjögreen
Keyword(s):  
Finite Difference ◽  
Multiple Scales ◽  
Finite Difference Methods ◽  
Propagation Speed ◽  
Two Dimensions ◽  
High Order ◽  
Reactive Flows ◽  
Fractional Step Method ◽  
High Order Finite Difference ◽  
Sr Method

AbstractIn this paper, we extend the high order finite-difference method with subcell resolution (SR) in [34] for two-species stiff one-reaction models to multispecies and multireaction inviscid chemical reactive flows, which are significantly more difficult because of the multiple scales generated by different reactions. For reaction problems, when the reaction time scale is very small, the reaction zone scale is also small and the governing equations become very stiff. Wrong propagation speed of discontinuity may occur due to the underresolved numerical solution in both space and time. The present SR method for reactive Euler system is a fractional step method. In the convection step, any high order shock-capturing method can be used. In the reaction step, an ODE solver is applied but with certain computed flow variables in the shock region modified by the Harten subcell resolution idea. Several numerical examples of multispecies and multireaction reactive flows are performed in both one and two dimensions. Studies demonstrate that the SR method can capture the correct propagation speed of discontinuities in very coarse meshes.

The Simulation of the Linearized Euler Equations by a Second Order Scheme is Possible

2005 ◽  
Vol 4 (1-2) ◽  
pp. 49-68
Author(s):  
R. Abgrall ◽  
M. Ravachol ◽  
S. Marret
Keyword(s):  
Numerical Simulation ◽  
Euler Equations ◽  
Finite Volume ◽  
Unstructured Meshes ◽  
High Order ◽  
Complex Geometries ◽  
Residual Distribution ◽  
Linearized Euler Equations ◽  
Order Scheme ◽  
The One

We are interested in the numerical simulation of acoustic perturbations via the linearized Euler equations using triangle unstructured meshes in complex geometries such as the one around a complete aircraft. It is known that the classical schemes using a finite volume formulation with high order extrapolation of the variables can be very disappointing. In this paper, we show that using an upwind residual distribution formulation, it is possible to simulate such problems, even on truly unstructured meshes. The main focus of the paper is on the propagative properties of the scheme.

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