Implicit scheme for meshless compressible Euler solver

Singh, Manish K.; Ramesh,; Balakrishnan, N.

doi:10.1080/19942060.2015.1048621

Cited by 5 publications

(2 citation statements)

References 31 publications

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“…The Jameson explicit scheme (Jameson et al, 1981;Ganzha and Vorozhtsov, 1996;Jameson and Baker, 1987;Singh et al, 2015) utilizes a Runge-Kutta multi-stage time integration (Jameson et al, 1981;Jeon et al, 2017) to the central discretization of the flux balance. This method involves a combination of efficient components such as dissipation terms, convergence acceleration and multigrid techniques (Ganzha and Vorozhtsov, 1996).…”

Section: Introductionmentioning

confidence: 99%

Kama Şekilli Kanat Üzerindeki Süpersonik Akışı Çözmek için Sayısal Bir Algoritma

Bakirci¹

2020

European Journal of Science and Technology

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In this paper, a new algorithm is developed to solve a two dimensional supersonic flow around a wedge-shaped airfoil. The MacCormack predictor-corrector method is utilized to develop a solution. To further investigate the flow properties, a numerical algorithm written in C++ has been compiled so that it may be compared to commercial softwares. The developed algorithm is compiled and run with the initial conditions of a free stream Mach number of 2 while the wedge angle is set at 15º. The compiled program revealed that the flow velocities increased without bound. Adjustment of this condition was achieved by adding artificial dissipation. The addition of dissipation term into the code resulted stable output and the presence of a shock. Same case was also simulated with ANSYS Fluent and CFL3D softwares using second order discretization.

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Section: Introductionmentioning

confidence: 99%

Kama Şekilli Kanat Üzerindeki Süpersonik Akışı Çözmek için Sayısal Bir Algoritma

Bakirci¹

2020

European Journal of Science and Technology

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“…In spite of the fact that the convergence speed achieved in the present test case is deemed satisfactory, it is important to say that more efficient convergence acceleration techniques would be required in view of larger application problems. Some interesting implicit and meshless multigrid approaches can be found in (Katz & Jameson, 2009b;Kennet, Timme, Angulo & Badcock, 2012;Singh, Ramesh & Balakrishnan, 2010).…”

Section: Numerical Resultsmentioning

confidence: 99%

Development and applications of the Finite Point Method to compressible aerodynamics problems

Ortega

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This work deals with the development and application of the Finite Point Method (FPM) to compressible aerodynamics problems. The research focuses mainly on investigating the capabilities of the meshless technique to address practical problems, one of the most outstanding issues in meshless methods. The FPM spatial approximation is studied firstly, with emphasis on aspects of the methodology that can be improved to increase its robustness and accuracy. Suitable ranges for setting the relevant approximation parameters and the performance likely to be attained in practice are determined. An automatic procedure to adjust the approximation parameters is also proposed to simplify the application of the method, reducing problem- and user-dependence without affecting the flexibility of the meshless technique. The discretization of the flow equations is carried out following wellestablished approaches, but drawing on the meshless character of the methodology. In order to meet the requirements of practical applications, the procedures are designed and implemented placing emphasis on robustness and efficiency (a simplification of the basic FPM technique is proposed to this end). The flow solver is based on an upwind spatial discretization of the convective fluxes (using the approximate Riemann solver of Roe) and an explicit time integration scheme. Two additional artificial diffusion schemes are also proposed to suit those cases of study in which computational cost is a major concern. The performance of the flow solver is evaluated in order to determine the potential of the meshless approach. The accuracy, computational cost and parallel scalability of the method are studied in comparison with a conventional FEM-based technique. Finally, practical applications and extensions of the flow solution scheme are presented. The examples provided are intended not only to show the capabilities of the FPM, but also to exploit meshless advantages. Automatic hadaptive procedures, moving domain and fluid-structure interaction problems, as well as a preliminary approach to solve high-Reynolds viscous flows, are a sample of the topics explored. All in all, the results obtained are satisfactorily accurate and competitive in terms of computational cost (if compared with a similar mesh-based implementation). This indicates that meshless advantages can be exploited with efficiency and constitutes a good starting point towards more challenging applications. En este trabajo se aborda el desarrollo del Método de Puntos Finitos (MPF) y su aplicación a problemas de aerodinámica de flujos compresibles. El objetivo principal es investigar el potencial de la técnica sin malla para la solución de problemas prácticos, lo cual constituye una de las limitaciones más importantes de los métodos sin malla. En primer lugar se estudia la aproximación espacial en el MPF, haciendo hincapié en aquéllos aspectos que pueden ser mejorados para incrementar la robustez y exactitud de la metodología. Se determinan rangos adecuados para el ajuste de los parámetros de la aproximación y su comportamiento en situaciones prácticas. Se propone además un procedimiento de ajuste automático de estos parámetros a fin de simplificar la aplicación del método y reducir la dependencia de factores como el tipo de problema y la intervención del usuario, sin afectar la flexibilidad de la técnica sin malla. A continuación se aborda el esquema de solución de las ecuaciones del flujo. La discretización de las mismas se lleva a cabo siguiendo métodos estándar, pero aprovechando las características de la técnica sin malla. Con el objetivo de abordar problemas prácticos, se pone énfasis en la robustez y eficiencia de la implementación numérica (se propone además una simplificación del procedimiento de solución). El comportamiento del esquema se estudia en detalle para evaluar su potencial y se analiza su exactitud, coste computacional y escalabilidad, todo ello en comparación con un método convencional basado en Elementos Finitos. Finalmente se presentan distintas aplicaciones y extensiones de la metodología desarrollada. Los ejemplos numéricos pretenden demostrar las capacidades del método y también aprovechar las ventajas de la metodología sin malla en áreas en que la misma puede ser de especial interés. Los problemas tratados incluyen, entre otras características, el refinamiento automático de la discretización, la presencia de fronteras móviles e interacción fluido-estructura, como así también una aplicación preliminar a flujos compresibles de alto número de Reynolds. Los resultados obtenidos muestran una exactitud satisfactoria. Además, en comparación con una técnica similar basada en Elementos Finitos, demuestran ser competitivos en términos del coste computacional. Esto indica que las ventajas de la metodología sin malla pueden ser explotadas con eficiencia, lo cual constituye un buen punto de partida para el desarrollo de ulteriores aplicaciones.

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A graphics processing unit-accelerated meshless method for two-dimensional compressible flows

Zhang

Chen

Cao

2017

Engineering Applications of Computational Fluid Mechanics

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A graphics processing unit (GPU) -accelerated meshless method is presented for solving twodimensional compressible flows over aerodynamic bodies. The Compute Unified Device Architecture (CUDA) Fortran programming model is employed to port the meshless method from central processing unit to GPU as a way of achieving efficiency, which involves implementation of CUDA kernels and management of data storage structure and thread hierarchy. The CUDA kernel subroutines are designed to meet with the point-based computing of the meshless method. The corresponding point-based data structure and thread hierarchy are constructed or manipulated in the paper by presenting two specific GPU implementations of the meshless method, which are developed for solving Navier-Stokes equations. The Jameson-Schmidt-Turkel scheme is used to estimate the flux terms of the Navier-Stokes equations and an explicit four-stage Runge-Kutta scheme is applied to update the solution at time level. After tuning the performances of the resulting two GPU-accelerated meshless solvers by changing the number of threads in a block, a set of typical flows over aerodynamic bodies are simulated for validation. Numerical results are shown in a comparison with available experimental data or computational values that appear in extant literature with an analysis of code performance. This reveals that the cost of computing time of the presented test cases is significantly reduced for both solvers without losing accuracy, while impressive speedups up to 64 times are achieved due to careful management of memory access. ARTICLE HISTORY

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Implicit scheme for meshless compressible Euler solver

Cited by 5 publications

References 31 publications

Kama Şekilli Kanat Üzerindeki Süpersonik Akışı Çözmek için Sayısal Bir Algoritma

Kama Şekilli Kanat Üzerindeki Süpersonik Akışı Çözmek için Sayısal Bir Algoritma

Development and applications of the Finite Point Method to compressible aerodynamics problems

A graphics processing unit-accelerated meshless method for two-dimensional compressible flows

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