Dissipation Improvement of MUSCL Scheme for Computational Aeroacoustics

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.

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Scattering of Waves by Two-Dimensional Circular Obstacles in Finite Water Depths

Journal of Ship Research ◽

10.5957/jsr.1979.23.1.32 ◽

1979 ◽

Vol 23 (01) ◽

pp. 32-42 ◽

Cited By ~ 1

Author(s):

Robert A. Naftzger ◽

Subrata K. Chakrabarti

Keyword(s):

Wave Interaction ◽

Wave Theory ◽

Finite Depth ◽

Wave Forces ◽

Linear Wave ◽

Two Dimensional ◽

Linear Wave Theory ◽

Dimensional Object ◽

Limiting Case ◽

Water Depths

The wave forces on a fixed two-dimensional object submerged in water of finite depth are obtained under the assumptions of linear wave theory. The far-field characteristics of the wave interaction with the object are also examined. The boundary-value problem for the wave potential is formulated in terms of Green's theorem, and the resulting integral equation is solved numerically. Results for a submerged and half-submerged circular cylinder and a bottom-seated half cylinder are presented. In the limiting case of infinite depth the numerical results compare quite well with known solutions.

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Numerical dissipation switch for two-dimensional central-upwind schemes

ESAIM Mathematical Modelling and Numerical Analysis ◽

10.1051/m2an/2021009 ◽

2021 ◽

Author(s):

Alexander Kurganov ◽

Yongle Liu ◽

Vladimir Zeitlin

Keyword(s):

Accurate Estimate ◽

Upwind Scheme ◽

Numerical Dissipation ◽

Computational Domain ◽

Two Dimensional ◽

Numerical Examples ◽

Upwind Schemes ◽

Local Propagation ◽

Contact Discontinuities

We propose a numerical dissipation switch, which helps to control the amount of numerical dissipation present in central-upwind schemes. Our main goal is to reduce the numerical dissipation without risking oscillations. This goal is achieved with the help of a more accurate estimate of the local propagation speeds in the parts of the computational domain, which are near contact discontinuities and shears. To this end, we introduce a switch parameter, which depends on the distributions of energy in the x- and y-directions. The resulting new central-upwind is tested on a number of numerical examples, which demonstrate the superiority of the proposed method over the original central-upwind scheme.

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

Communications in Computational Physics ◽

10.4208/cicp.scpde14.43s ◽

2016 ◽

Vol 19 (5) ◽

pp. 1111-1140 ◽

Cited By ~ 19

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.

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Modifications of the Godunov method for computing disturbance propagation in an elastic body

Proceedings of the Mavlyutov Institute of Mechanics ◽

10.21662/uim2016.1.018 ◽

2016 ◽

Vol 11 (1) ◽

pp. 119-126 ◽

Cited By ~ 4

Author(s):

A.A. Aganin ◽

N.A. Khismatullina

Keyword(s):

Elastic Body ◽

Godunov Method ◽

Two Dimensional ◽

Dimensional Problem ◽

Order Accuracy ◽

One Dimensional ◽

Disturbance Propagation ◽

Linear Waves ◽

Longitudinal And Shear Waves ◽

Contact Discontinuities

Numerical investigation of efficiency of UNO- and TVD-modifications of the Godunov method of the second order accuracy for computation of linear waves in an elastic body in comparison with the classical Godunov method is carried out. To this end, one-dimensional cylindrical Riemann problems are considered. It is shown that the both modifications are considerably more accurate in describing radially converging as well as diverging longitudinal and shear waves and contact discontinuities both in one- and two-dimensional problem statements. At that the UNO-modification is more preferable than the TVD-modification because exact implementation of the TVD property in the TVD-modification is reached at the expense of “cutting” solution extrema.

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