scholarly journals Applications and Spectral Analysis of some Optimized High Order Low Dispersion and Low Dissipation Schemes

2014 ◽  
Vol 8 (3) ◽  
pp. 993-1001
Author(s):  
Appanah Rao Appadu
Keyword(s):  
Spectral Analysis ◽  
High Order ◽  
Low Dissipation ◽  
Low Dispersion

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.

High-order low-dissipation low-dispersion diagonally implicit Runge–Kutta schemes

2015 ◽  
Vol 286 ◽  
pp. 38-48 ◽  
Author(s):  
Farshid Nazari ◽  
Abdolmajid Mohammadian ◽  
Martin Charron
Keyword(s):  
High Order ◽  
Low Dissipation ◽  
Runge Kutta ◽  
Low Dispersion

scholarly journals Compressible Flow Simulation with Moving Geometries using the Brinkman Penalization in High-Order Discontinuous Galerkin

2020 ◽  
Author(s):  
Neda Ebrahimi Pour ◽  
Nikhil Anand ◽  
Harald Klimach ◽  
Sabine Roller
Keyword(s):  
Degrees Of Freedom ◽  
Flow Simulation ◽  
High Order ◽  
Three Dimensions ◽  
Limiting Factor ◽  
Moving Wall ◽  
Low Dissipation ◽  
Computational Mesh ◽  
Penalization Technique ◽  
Discontinous Galerkin

Abstract In this work we investigate the Brinkman volume penalization technique in the context of a high-order Discontinous Galerkin method to model moving wall boundaries for compressible fluid flow simulations. High-order approximations are especially of interest as they require few degrees of freedom to represent smooth solutions accurately. This reduced memory consumption is attractive on modern computing systems where the memory bandwidth is a limiting factor. Due to their low dissipation and dispersion they are also of particular interest for aeroacoustic problems. However, a major problem for the high-order discretization is the appropriate representation of wall geometries. In this work we look at the Brinkman penalization technique, which addresses this problem and allows the representation of geometries without modifying the computational mesh. The geometry is modelled as an artificial porous medium and embedded in the equations. As the mesh is independent of the geometry with this method, it is not only well suited for highorder discretizations but also for problems where the obstacles are moving.We look into the deployment of this strategy by briefly discussing the Brinkman penalization technique and its application in our solver and investigate its behavior in fundamental one-dimensional setups, such as shock reflection at a moving wall and the formation of a shock in front of a piston. This is followed by the application to setups with two and three dimensions, illustrating the method in the presence of curved surfaces.

Development and Application of Variational Methods for Simulation of Miscible Displacement in Porous Media

1977 ◽  
Vol 17 (03) ◽  
pp. 228-246 ◽  
Author(s):  
A. Settari ◽  
H.S. Price ◽  
T. Dupont
Keyword(s):  
Finite Difference ◽  
Miscible Displacement ◽  
High Order ◽  
Numerical Dispersion ◽  
Convection Diffusion ◽  
Finite Difference Approximations ◽  
Variational Approximations ◽  
Difference Approximations ◽  
Low Dispersion ◽  
Finite Difference Techniques

Abstract Many reservoir engineering problems involve solving fluid flow equations whose solutions are characterized by sharp fronts and low dispersion levels. This is particularly important in tracking small slugs that are characteristic of chemical floods, polymer floods, first- and multiple-contact hydrocarbon miscible polymer floods, first- and multiple-contact hydrocarbon miscible displacements, and most thermal processes. The use of finite-difference approximations to solve these problems when low dispersion levels and small slugs need to be modeled accurately may be prohibitively expensive. This paper shows that the use of high-order variational approximations is a very effective means for economically solving these problems. This paper presents some numerical results that demonstrate that high-order variational methods can be used to solve two-dimensional reservoir engineering problems where finite-difference approximations would require 104 problems where finite-difference approximations would require 104 to 105 blocks. The variational solutions are shown to be essentially insensitive to grid orientation for unfavorable mobility ratios up to M = 100. Introduction The equations describing miscible displacement in a porous medium (convection-diffusion equations) are among the more difficult to solve by numerical means. The character of the concentration equation ranges from parabolic to almost hyperbolic depending on the ratio of convection to diffusion (Peclet number). Consequently, the finite-difference techniques developed for solving the convection diffusion problem can be divided into two categories: those solving the problem as parabolic and those treating the problem as hyperbolic. The parabolic techniques are unsatisfactory when the diffusion becomes small compared with the convection. The methods using central difference approximations for the convection terms oscillate. Price et al. have shown that these oscillations can be eliminated only by using small spatial increments. Methods using upstream difference approximations do not oscillate, but they introduce large truncation errors that have the character of a large diffusion term. Lantz has shown that for many practical problems, reducing the magnitude of numerical dispersion problems, reducing the magnitude of numerical dispersion sufficiently so that it does not mask the physical dispersion will force an impractically fine grid. Several improvements have been suggested, such as transfer of overshoots truncation-error cancellation, and two-point upstream approximations; but none of these is quite satisfactory in the general case. The hyperbolic methods (method of characteristics, point tracking, etc.) also pose many practical problems. These include the complex treatment required for sources and sinks, the need to redistribute points continually when modeling converging and diverging flow, the problem of maintaining a material balance, problems created by complex geometries, and the practical limitation problems created by complex geometries, and the practical limitation of the time-step size. Moreover, these schemes cannot be shown to converge, thereby making the choice of grid size and point distribution fairly arbitrary. Finally, many nonlinearities, such as reactions and adsorption, need to be treated point-by-point, requiring large amounts of computer time and storage. Because the major difficulty in solving the miscible displacement problem is the determination of an accurate approximation to a very sharp concentration front, one of the most promising alternatives to the schemes mentioned above is the use of promising alternatives to the schemes mentioned above is the use of high-order variational approximations, such as those proposed by Ciarlet et al. These methods (which include Galerkin and finite-element methods) are potentially far more accurate for a given amount of computation than the standard finite-difference techniques and, therefore, more able to solve problems that would otherwise be impractical. SPEJ P. 228

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