Geometry, Energy, and Entropy Compatible (GEEC) Variational Approaches to Various Numerical Schemes for Fluid Dynamics

2019 ◽  
pp. 559-567
Author(s):  
Antoine Llor ◽  
Thibaud Vazquez-Gonzalez
Keyword(s):  
Fluid Dynamics ◽  
Numerical Schemes ◽  
Variational Approaches

Adaptive LMR Simulation of DDT in Obstructed Channel

2016 ◽  
Author(s):  
Ke Ren ◽  
Alexei Kotchourko ◽  
Alexander Lelyakin
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Computer Technology ◽  
Mesh Refinement ◽  
Direct Methods ◽  
Physical Models ◽  
Current Work ◽  
Numerical Schemes ◽  
Deflagration To Detonation Transition ◽  
Detonation Transition

Deflagration to detonation transition (DDT) is a challenging subject in computational fluid dynamics both from a standpoint of the phenomenon nature understanding and from extremely demanding computational efforts. In recent years, as the development of computer technology and improvement of numerical schemes was achieved, some more direct methods have been found to reproduce the DDT mechanistically without additional numerical or physical models. In the current work, highly resolved DDT simulations of hydrogen-air and of hydrogen-oxygen mixtures in 2D channel with regular repeating obstacles are present. The technique of local mesh refinement (ALMR) is implemented in the simulations to minimize the computational efforts. The criteria for the ALMR are examined and optimized in simulations.

scholarly journals The Technique of MIEELDLD in Computational Aeroacoustics

2012 ◽  
Vol 2012 ◽  
pp. 1-30
Author(s):  
A. R. Appadu
Keyword(s):  
Fluid Dynamics ◽  
High Order ◽  
Computational Aeroacoustics ◽  
Advection Equation ◽  
Optimal Parameters ◽  
Numerical Schemes ◽  
Low Dissipation ◽  
Linear Advection Equation ◽  
Discretization Schemes ◽  
Low Dispersion

The numerical simulation of aeroacoustic phenomena requires high-order accurate numerical schemes with low dispersion and low dissipation errors. A technique has recently been devised in a Computational Fluid Dynamics framework which enables optimal parameters to be chosen so as to better control the grade and balance of dispersion and dissipation in numerical schemes (Appadu and Dauhoo, 2011; Appadu, 2012a; Appadu, 2012b; Appadu, 2012c). This technique has been baptised as the Minimized Integrated Exponential Error for Low Dispersion and Low Dissipation (MIEELDLD) and has successfully been applied to numerical schemes discretising the 1-D, 2-D, and 3-D advection equations. In this paper, we extend the technique of MIEELDLD to the field of computational aeroacoustics and have been able to construct high-order methods with Low Dispersion and Low Dissipation properties which approximate the 1-D linear advection equation. Modifications to the spatial discretization schemes designed by Tam and Webb (1993), Lockard et al. (1995), Zingg et al. (1996), Zhuang and Chen (2002), and Bogey and Bailly (2004) have been obtained, and also a modification to the temporal scheme developed by Tam et al. (1993) has been obtained. These novel methods obtained using MIEELDLD have in general better dispersive properties as compared to the existing optimised methods.

scholarly journals CFD Julia: A Learning Module Structuring an Introductory Course on Computational Fluid Dynamics

Fluids ◽  
2019 ◽  
Vol 4 (3) ◽  
pp. 159 ◽  
Author(s):  
Suraj Pawar ◽  
Omer San
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Finite Difference ◽  
Stokes Equations ◽  
Iterative Solvers ◽  
Navier Stokes ◽  
Finite Difference Schemes ◽  
Two Dimensional ◽  
Numerical Schemes ◽  
Computational Performance

CFD Julia is a programming module developed for senior undergraduate or graduate-level coursework which teaches the foundations of computational fluid dynamics (CFD). The module comprises several programs written in general-purpose programming language Julia designed for high-performance numerical analysis and computational science. The paper explains various concepts related to spatial and temporal discretization, explicit and implicit numerical schemes, multi-step numerical schemes, higher-order shock-capturing numerical methods, and iterative solvers in CFD. These concepts are illustrated using the linear convection equation, the inviscid Burgers equation, and the two-dimensional Poisson equation. The paper covers finite difference implementation for equations in both conservative and non-conservative form. The paper also includes the development of one-dimensional solver for Euler equations and demonstrate it for the Sod shock tube problem. We show the application of finite difference schemes for developing two-dimensional incompressible Navier-Stokes solvers with different boundary conditions applied to the lid-driven cavity and vortex-merger problems. At the end of this paper, we develop hybrid Arakawa-spectral solver and pseudo-spectral solver for two-dimensional incompressible Navier-Stokes equations. Additionally, we compare the computational performance of these minimalist fashion Navier-Stokes solvers written in Julia and Python.

scholarly journals Schemes with Well-Controlled Dissipation. Hyperbolic Systems in Nonconservative Form

2017 ◽  
Vol 21 (4) ◽  
pp. 913-946 ◽  
Author(s):  
Abdelaziz Beljadid ◽  
Philippe G. LeFloch ◽  
Siddhartha Mishra ◽  
Carlos Parés
Keyword(s):  
Fluid Dynamics ◽  
Numerical Method ◽  
Linear Stability ◽  
Weak Solutions ◽  
Hyperbolic Systems ◽  
Small Scale ◽  
Numerical Schemes ◽  
Nonconservative System ◽  
Complex Fluid ◽  
Nonlinear Hyperbolic Systems

AbstractWe propose here a class of numerical schemes for the approximation of weak solutions to nonlinear hyperbolic systems in nonconservative form—the notion of solution being understood in the sense of Dal Maso, LeFloch, and Murat (DLM). The proposed numerical method falls within LeFloch-Mishra's framework of schemes with well-controlled dissipation (WCD), recently introduced for dealing with small-scale dependent shocks. We design WCD schemes which are consistent with a given nonconservative system at arbitrarily high-order and then analyze their linear stability. We then investigate several nonconservative hyperbolic models arising in complex fluid dynamics, and we numerically demonstrate the convergence of our schemes toward physically meaningful weak solutions.

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