Higher-Order Godunov Methods for Reducing Numerical Dispersion in Reservoir Simulation

1985 ◽  
Author(s):  
J.B. Bell ◽  
G.R. Shubin
Keyword(s):  
Reservoir Simulation ◽  
Higher Order ◽  
Numerical Dispersion ◽  
Godunov Methods

Directly Simulation of Second Order Hyperbolic Systems in Second Order Form via the Regularization Concept

2016 ◽  
Vol 20 (1) ◽  
pp. 86-135 ◽  
Author(s):  
Hassan Yousefi ◽  
Seyed Shahram Ghorashi ◽  
Timon Rabczuk
Keyword(s):  
Hyperbolic Systems ◽  
Higher Order ◽  
Second Order ◽  
Numerical Dispersion ◽  
Stress Wave Propagation ◽  
Finite Difference Schemes ◽  
Sampled Data ◽  
Discontinuous Solutions ◽  
Order Form ◽  
Spurious Oscillations

AbstractWe present an efficient and robust method for stress wave propagation problems (second order hyperbolic systems) having discontinuities directly in their second order form. Due to the numerical dispersion around discontinuities and lack of the inherent dissipation in hyperbolic systems, proper simulation of such problems are challenging. The proposed idea is to denoise spurious oscillations by a post-processing stage from solutions obtained from higher-order grid-based methods (e.g., high-order collocation or finite-difference schemes). The denoising is done so that the solutions remain higher-order (here, second order) around discontinuities and are still free from spurious oscillations. For this purpose, improved Tikhonov regularization approach is advised. This means to let data themselves select proper denoised solutions (since there is no pre-assumptions about regularized results). The improved approach can directly be done on uniform or non-uniform sampled data in a way that the regularized results maintenance continuous derivatives up to some desired order. It is shown how to improve the smoothing method so that it remains conservative and has local estimating feature. To confirm effectiveness of the proposed approach, finally, some one and two dimensional examples will be provided. It will be shown how both the numerical (artificial) dispersion and dissipation can be controlled around discontinuous solutions and stochastic-like results.

A New Approach for Reducing Numerical Dispersion in Reservoir Simulation

2017 ◽  
Author(s):  
B. Kayode ◽  
S. Surdiman ◽  
Z. Ghareeb ◽  
H. Salem
Keyword(s):  
Reservoir Simulation ◽  
Numerical Dispersion ◽  
New Approach

Numerical Study of Advection Schemes for Interface Capturing in a Volume of Fluid Method on Unstructured Meshes

2011 ◽  
Author(s):  
Hua Shan ◽  
Sung-Eun Kim
Keyword(s):  
Free Surface ◽  
Volume Fraction ◽  
Numerical Study ◽  
Volume Of Fluid ◽  
Unstructured Meshes ◽  
Higher Order ◽  
Numerical Dispersion ◽  
Numerical Dissipation ◽  
Interface Capturing ◽  
Advection Schemes

In solving naval hydrodynamics problems using computational fluid dynamics (CFD), the moving free surface between air and water introduces extra difficulties to numerical methods, since the material property jumps across the interface and the time-dependent free surface position becomes part of the solution. Engineering applications often require a flexible and robust solver for incompressible multi-phase viscous flows with the capability of capturing the interface. In the volume of fluid (VOF) method, the interface is captured by directly solving the convection transport equation of volume fraction. In this case, the numerical dissipation of the advection scheme smears the sharp interface and the numerical dispersion causes unphysical oscillations near the interface. Utilizing the guidance of boundedness criteria, many limited higher-order non-liner advection schemes have been developed in an attempt to balance numerical dissipation and dispersion. Though it is well-known that these non-linear advection schemes can lead to solutions combining boundednesss and accuracy, users are often overwhelmed by the wide variety of available schemes. Also, these schemes are developed with the assumption of a uniform Cartesian-type mesh. Thus, a thorough investigation and comparison of the performance of these interface-capturing advection schemes are necessary, especially for naval hydrodynamics problems solved on unstructured meshes. In this study, a systematic comparison and evaluation of several existing and new bounded, higher-order advection schemes has been conducted within the framework of NavyFOAM, which is developed based on OpenFOAM — an object orientated C++ toolbox for the customization and extension of numerical solvers for continuum mechanics problems, including CFD, where the governing equations are discretized using the cell-centered finite volume method on unstructured mesh. The flexible infrastructure of the code enables us to implement and test the selected advection schemes very quickly. The test cases include advection of hollow cylinders, Zalesak’s rotating slotted disk, traveling solitary wave, dam breaking problem.

The Use of Higher-Order Differencing Techniques in Reservoir Simulation

1987 ◽  
Vol 2 (03) ◽  
pp. 360-372 ◽  
Author(s):  
I.J. Taggart ◽  
W.V. Pinczewski
Keyword(s):  
Reservoir Simulation ◽  
Higher Order
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