scholarly journals High-Order and High Accurate CFD Methods and Their Applications for Complex Grid Problems

2012 ◽  
Vol 11 (4) ◽  
pp. 1081-1102 ◽  
Author(s):  
Xiaogang Deng ◽  
Meiliang Mao ◽  
Guohua Tu ◽  
Hanxin Zhang ◽  
Yifeng Zhang
Keyword(s):  
Delta Wing ◽  
Rapid Development ◽  
High Order ◽  
Interface Condition ◽  
Finite Difference Schemes ◽  
High Order Schemes ◽  
Flow Problems ◽  
Fifth Order ◽  
High Order Finite Difference ◽  
Double Delta Wing

AbstractThe purpose of this article is to summarize our recent progress in high-order and high accurate CFD methods for flow problems with complex grids as well as to discuss the engineering prospects in using these methods. Despite the rapid development of high-order algorithms in CFD, the applications of high-order and high accurate methods on complex configurations are still limited. One of the main reasons which hinder the widely applications of these methods is the complexity of grids. Many aspects which can be neglected for low-order schemes must be treated carefully for high-order ones when the configurations are complex. In order to implement high-order finite difference schemes on complex multi-block grids, the geometric conservation law and block-interface conditions are discussed. A conservative metric method is applied to calculate the grid derivatives, and a characteristic-based interface condition is employed to fulfil high-order multi-block computing. The fifth-order WCNS-E-5 proposed by Deng is applied to simulate flows with complex grids, including a double-delta wing, a transonic airplane configuration, and a hypersonic X-38 configuration. The results in this paper and the references show pleasant prospects in engineering-oriented applications of high-order schemes.

High Order Schemes on Three-Dimensional General Polyhedral Meshes — Application to the Level Set Method

2012 ◽  
Vol 12 (1) ◽  
pp. 1-41 ◽  
Author(s):  
Thibault Pringuey ◽  
R. Stewart Cant
Keyword(s):  
Level Set ◽  
Three Dimensional ◽  
Unstructured Meshes ◽  
High Order ◽  
Convex Polyhedra ◽  
Two Phase ◽  
High Order Schemes ◽  
Flow Problems ◽  
Mixed Element ◽  
Areas Of Interest

AbstractIn this article, we detail the methodology developed to construct arbitrarily high order schemes — linear and WENO — on 3D mixed-element unstructured meshes made up of general convex polyhedral elements. The approach is tailored specifically for the solution of scalar level set equations for application to incompressible two-phase flow problems. The construction of WENO schemes on 3D unstructured meshes is notoriously difficult, as it involves a much higher level of complexity than 2D approaches. This due to the multiplicity of geometrical considerations introduced by the extra dimension, especially on mixed-element meshes. Therefore, we have specifically developed a number of algorithms to handle mixed-element meshes composed of convex polyhedra with convex polygonal faces. The contribution of this work concerns several areas of interest: the formulation of an improved methodology in 3D, the minimisation of computational runtime in the implementation through the maximum use of pre-processing operations, the generation of novel methods to handle complex 3D mixed-element meshes and finally the application of the method to the transport of a scalar level set.

High-order finite difference WENO schemes with positivity-preserving limiter for correlated random walk with density-dependent turning rates

2015 ◽  
Vol 25 (08) ◽  
pp. 1553-1588 ◽  
Author(s):  
Yan Jiang ◽  
Chi-Wang Shu ◽  
Mengping Zhang
Keyword(s):  
Random Walk ◽  
Finite Difference ◽  
Temporal Integration ◽  
Time Discretization ◽  
High Order ◽  
Correlated Random Walk ◽  
Third Order ◽  
Positivity Preserving ◽  
Fifth Order ◽  
High Order Finite Difference

In this paper, we discuss high-order finite difference weighted essentially non-oscillatory schemes, coupled with total variation diminishing (TVD) Runge–Kutta (RK) temporal integration, for solving the semilinear hyperbolic system of a correlated random walk model describing movement of animals and cells in biology. Since the solutions to this system are non-negative, we discuss a positivity-preserving limiter without compromising accuracy. Analysis is performed to justify the maintenance of third-order spatial/temporal accuracy when the limiters are applied to a third-order finite difference scheme and third-order TVD-RK time discretization for solving this model. Numerical results are also provided to demonstrate these methods up to fifth-order accuracy.

scholarly journals Comparative Study of Three High Order Schemes for LES of Temporally Evolving Mixing Layers

2012 ◽  
Vol 12 (5) ◽  
pp. 1603-1622 ◽  
Author(s):  
Helen C. Yee ◽  
Bjorn Sjögreen ◽  
Abdellah Hadjadj
Keyword(s):  
High Order ◽  
Mixing Layers ◽  
Compressible Turbulence ◽  
Filter Method ◽  
Eighth Order ◽  
Base Scheme ◽  
High Order Schemes ◽  
Supersonic Regime ◽  
Seventh Order ◽  
Fifth Order

AbstractThree high order shock-capturing schemes are compared for large eddy simulations (LES) of temporally evolving mixing layers for different convective Mach numbers ranging from the quasi-incompressible regime to highly compressible supersonic regime. The considered high order schemes are fifth-order WENO (WENO5), seventh-order WENO (WENO7) and the associated eighth-order central spatial base scheme with the dissipative portion of WENO7 as a nonlinear post-processing filter step (WENO7fi). This high order nonlinear filter method of Yee & Sjögreen is designed for accurate and efficient simulations of shock-free compressible turbulence, turbulence with shocklets and turbulence with strong shocks with minimum tuning of scheme parameters. The LES results by WENO7fi using the same scheme parameter agree well with experimental results compiled by Barone et al., and published direct numerical simulations (DNS) work of Rogers & Moser and Pantano & Sarkar, whereas results by WENO5 and WENO7 compare poorly with experimental data and DNS computations.

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