scholarly journals Numerical dissipation switch for two-dimensional central-upwind schemes

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.

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.

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

2016 ◽  
Vol 11 (1) ◽  
pp. 119-126 ◽  
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.

Methods to Accelerate Ray Tracing in the Monte Carlo Method for Surface-to-Surface Radiation Transport

2006 ◽  
Vol 128 (9) ◽  
pp. 945-952 ◽  
Author(s):  
Sandip Mazumder
Keyword(s):  
Monte Carlo ◽  
Ray Tracing ◽  
Radiation Transport ◽  
Three Dimensional ◽  
Intersection Point ◽  
Surface Radiation ◽  
Computational Domain ◽  
Two Dimensional ◽  
Spatial Partitioning ◽  
The Monte Carlo Method

Two different algorithms to accelerate ray tracing in surface-to-surface radiation Monte Carlo calculations are investigated. The first algorithm is the well-known binary spatial partitioning (BSP) algorithm, which recursively bisects the computational domain into a set of hierarchically linked boxes that are then made use of to narrow down the number of ray-surface intersection calculations. The second algorithm is the volume-by-volume advancement (VVA) algorithm. This algorithm is new and employs the volumetric mesh to advance the ray through the computational domain until a legitimate intersection point is found. The algorithms are tested for two classical problems, namely an open box, and a box in a box, in both two-dimensional (2D) and three-dimensional (3D) geometries with various mesh sizes. Both algorithms are found to result in orders of magnitude gains in computational efficiency over direct calculations that do not employ any acceleration strategy. For three-dimensional geometries, the VVA algorithm is found to be clearly superior to BSP, particularly for cases with obstructions within the computational domain. For two-dimensional geometries, the VVA algorithm is found to be superior to the BSP algorithm only when obstructions are present and are densely packed.

Two Dimensional Simulations of Enhanced Heat Transfer in an Intermittently Grooved Channel

2000 ◽  
Author(s):  
M. Greiner ◽  
P. F. Fischer ◽  
H. M. Tufo
Keyword(s):  
Heat Transfer ◽  
Local Heat Transfer ◽  
Spectral Element ◽  
Local Heat ◽  
Navier Stokes ◽  
Computational Domain ◽  
Two Dimensional ◽  
Number Range ◽  
Element Technique ◽  
Outflow Boundary

Abstract Two-dimensional Navier-Stokes simulations of heat and momentum transport in an intermittently grooved passage are performed using the spectral element technique for the Reynolds number range 600 ≤ Re ≤ 1800. The computational domain has seven contiguous transverse grooves cut symmetrically into opposite walls, followed by a flat section with the same length. Periodic inflow/outflow boundary conditions are employed. The development and decay of unsteady flow is observed in the grooved and flat sections, respectively. The axial variation of the unsteady component of velocity is compared to the local heat transfer, shear stress and pressure gradient. The results suggest that intermittently grooved passages may offer even higher heat transfer for a given pumping power than the levels observed in fully grooved passages.

scholarly journals On the Interior Stress Problem for Elastic Bodies

2000 ◽  
Vol 67 (4) ◽  
pp. 658-662 ◽  
Author(s):  
J. Helsing
Keyword(s):  
Integral Equation ◽  
Computational Domain ◽  
Original Formulation ◽  
Unknown Quantity ◽  
Numerical Examples ◽  
Stress Problem ◽  
Elastic Bodies ◽  
Interior Stress

The classic Sherman-Lauricella integral equation and an integral equation due to Muskhelishvili for the interior stress problem are modified. The modified formulations differ from the classic ones in several respects: Both modifications are based on uniqueness conditions with clear physical interpretations and, more importantly, they do not require the arbitrary placement of a point inside the computational domain. Furthermore, in the modified Muskhelishvili equation the unknown quantity, which is solved for, is simply related to the stress. In Muskhelishvili’s original formulation the unknown quantity is related to the displacement. Numerical examples demonstrate the greater stability of the modified schemes. [S0021-8936(00)01304-0]

Numerical solution of two-dimensional first kind Fredholm integral equations by using linear Legendre wavelet

2016 ◽  
Vol 14 (01) ◽  
pp. 1650004 ◽  
Author(s):  
M. Tahami ◽  
A. Askari Hemmat ◽  
S. A. Yousefi
Keyword(s):  
Integral Equation ◽  
Tensor Product ◽  
Numerical Solution ◽  
Fredholm Integral Equation ◽  
Fredholm Integral Equations ◽  
Wavelet Basis ◽  
Two Dimensional ◽  
Legendre Wavelets ◽  
Numerical Examples ◽  
One Dimensional

In one-dimensional problems, the Legendre wavelets are good candidates for approximation. In this paper, we present a numerical method for solving two-dimensional first kind Fredholm integral equation. The method is based upon two-dimensional linear Legendre wavelet basis approximation. By applying tensor product of one-dimensional linear Legendre wavelet we construct a two-dimensional wavelet. Finally, we give some numerical examples.

scholarly journals Parameter Identification in the Two-Dimensional Riesz Space Fractional Diffusion Equation

2020 ◽  
Vol 4 (3) ◽  
pp. 39
Author(s):  
Rafał Brociek ◽  
Agata Chmielowska ◽  
Damian Słota
Keyword(s):  
Differential Equation ◽  
Diffusion Equation ◽  
Parameter Identification ◽  
Fractional Diffusion ◽  
Riesz Space ◽  
Fractional Diffusion Equation ◽  
Two Dimensional ◽  
Numerical Examples ◽  
Space Fractional Diffusion Equation ◽  
Swarm Intelligence Algorithm

This paper presents the application of the swarm intelligence algorithm for solving the inverse problem concerning the parameter identification. The paper examines the two-dimensional Riesz space fractional diffusion equation. Based on the values of the function (for the fixed points of the domain) which is the solution of the described differential equation, the order of the Riesz derivative and the diffusion coefficient are identified. The paper includes numerical examples illustrating the algorithm’s accuracy.

Two‐dimensional acoustic modeling by a hybrid method

Geophysics ◽  
1985 ◽  
Vol 50 (8) ◽  
pp. 1273-1284 ◽  
Author(s):  
V. Shtivelman
Keyword(s):  
Wave Propagation ◽  
Wave Field ◽  
Inhomogeneous Medium ◽  
Hybrid Method ◽  
Wave Scattering ◽  
Acoustic Modeling ◽  
Two Dimensional ◽  
Numerical Techniques ◽  
Numerical Examples ◽  
Field Computation

This paper follows previous work (Shtivelman, 1984) in which a hybrid method for wave‐field computation was developed. The method combines analytical and numerical techniques and is based upon separation of the processes of wave scattering and wave propagation. The method is further developed and improved; particularly, it is generalized for the case of an inhomogeneous medium above scattering objects (provided the inhomogeneity is weak, i.e., the effects of scattering can be neglected) and is represented by a simpler and more convenient form. Several numerical examples illustrating application of the method to the problems of two‐dimensional acoustic modeling are considered.

A Stable Mass-Flow-Weighted Two-Dimensional Skew Upwind Scheme

1983 ◽  
Vol 6 (4) ◽  
pp. 395-408 ◽  
Author(s):  
Yassin Hassan ◽  
James Rice ◽  
J. H. Kim
Keyword(s):  
Mass Flow ◽  
Upwind Scheme ◽  
Two Dimensional
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