Entropy Stable Scheme on Two-Dimensional Unstructured Grids for Euler Equations

2016 ◽  
Vol 19 (5) ◽  
pp. 1111-1140 ◽  
Author(s):  
Deep Ray ◽  
Praveen Chandrashekar ◽  
Ulrik S. Fjordholm ◽  
Siddhartha Mishra
Keyword(s):  
High Resolution ◽  
Euler Equations ◽  
Compressible Flows ◽  
Unstructured Grids ◽  
Numerical Dissipation ◽  
Finite Volume Scheme ◽  
Two Dimensional ◽  
Complex Flow ◽  
Reconstruction Procedure ◽  
Entropy Stable

AbstractWe propose an entropy stable high-resolution finite volume scheme to approximate systems of two-dimensional symmetrizable conservation laws on unstructured grids. In particular we consider Euler equations governing compressible flows. The scheme is constructed using a combination of entropy conservative fluxes and entropy-stable numerical dissipation operators. High resolution is achieved based on a linear reconstruction procedure satisfying a suitable sign property that helps to maintain entropy stability. The proposed scheme is demonstrated to robustly approximate complex flow features by a series of benchmark numerical experiments.

Dissipation Improvement of MUSCL Scheme for Computational Aeroacoustics

2001 ◽  
Vol 17 (1) ◽  
pp. 39-47
Author(s):  
San-Yin Lin ◽  
Sheng-Chang Shih ◽  
Jen-Jiun Hu
Keyword(s):  
Wave Interaction ◽  
Sine Wave ◽  
Numerical Dissipation ◽  
Finite Volume Scheme ◽  
Linear Wave ◽  
Riemann Solver ◽  
Two Dimensional ◽  
Order Accuracy ◽  
Upwind Schemes ◽  
Continuous Waves

ABSTRACTAn upwind finite-volume scheme is studied for solving the solutions of two dimensional Euler equations. It based on the MUSCL (Monotone Upstream Scheme for Conservation Laws) approach with the Roe approximate Riemann solver for the numerical flux evaluation. First, dissipation and dispersion relation, and group velocity of the scheme are derived to analyze the capability of the proposed scheme for capturing physical waves, such as acoustic, entropy, and vorticity waves. Then the scheme is greatly enhanced through a strategy on the numerical dissipation to effectively handle aeroacoustic computations. The numerical results indicate that the numerical dissipation strategy allows that the scheme simulates the continuous waves, such as sound and sine waves, at fourth-order accuracy and captures the discontinuous waves, such a shock wave, sharply as well as most of upwind schemes do. The tested problems include linear wave convection, propagation of a sine-wave packet, propagation of discontinuous and sine waves, shock and sine wave interaction, propagation of acoustic, vorticity, and density pulses in an uniform freestream, and two-dimensional traveling vortex in a low-speed freestream.

A New Agglomeration Method for Isotropic Unstructured Grids

2012 ◽  
Vol 241-244 ◽  
pp. 2957-2961
Author(s):  
Zong Zhe Li ◽  
Zheng Hua Wang ◽  
Wei Cao ◽  
Lu Yao
Keyword(s):  
Aspect Ratio ◽  
Euler Equations ◽  
Multigrid Method ◽  
Unstructured Grid ◽  
Convergence Rates ◽  
Unstructured Grids ◽  
Common Vertex ◽  
Finite Volume Scheme ◽  
High Quality ◽  
Coarse Grids

A robust aspect ratio based agglomeration algorithm to generate high quality coarse grids for unstructured grid is proposed in this paper. The algorithm focuses on multigrid techniques for the numerical solution of Euler equations, which conform to cell-centered finite volume scheme, combines isotropic vertex-based agglomeration to yield large increases in convergence rates. Aspect ratio is used as fusing weight to capture the degree of cell convexity and give an indication of cell quality, agglomerating isotropic cells sharing a common vertex. Consequently, we conduct agglomeration multigrid method to solve Euler equations on 2D isotropic unstructured grid, and compare the results with MGridGen

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