Low-Diffusion Rotated Upwind Schemes, Multigrid and Defect Correction for Steady, Multi-Dimensional Euler Flows

Koren, Barry

doi:10.1007/978-3-0348-5712-3_19

Cited by 12 publications

(25 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Overall, the Flat scheme shows the least grid dependency. (Roe & Sidilkover, 1992), the CTU scheme (Collela, 1990) and Koren's scheme (Koren, 1991) Common Name (c) Koren'…”

Section: Experimentation and Discussionmentioning

confidence: 99%

Industrial Compositional Streamline Simulation for Efficient and Accurate Prediction of Gas Injection and WAG Processes

Gerritsen¹

2008

View full text Add to dashboard Cite

Executive SummaryGas-injection processes are widely and increasingly used for enhanced oil recovery (EOR). In the United States, for example, EOR production by gas injection accounts for approximately 45% of total EOR production and has tripled since 1986. The understanding of the multiphase, multicomponent flow taking place in any displacement process is essential for successful design of gas-injection projects. Due to complex reservoir geometry, reservoir fluid properties and phase behavior, the design of accurate and efficient numerical simulations for the multiphase, multicomponent flow governing these processes is nontrivial. In this work, we developed, implemented and tested a streamline based solver for gas injection processes that is computationally very attractive: as compared to traditional Eulerian solvers in use by industry it computes solutions with a computational speed orders of magnitude higher and a comparable accuracy provided that cross-flow effects do not dominate. We contributed to the development of compositional streamline solvers in three significant ways: improvement of the overall framework allowing improved streamline coverage and partial streamline tracing, amongst others; parallelization of the streamline code, which significantly improves wall clock time; and development of new compositional solvers that can be implemented along streamlines as well as in existing Eulerian codes used by industry.We designed several novel ideas in the streamline framework. First, we developed an adaptive streamline coverage algorithm. Adding streamlines locally can reduce computational costs by concentrating computational efforts where needed, and reduce mapping errors. Adapting streamline coverage effectively controls mass balance errors that mostly result from the mapping from streamlines to pressure grid. We also introduced the concept of partial streamlines: streamlines that do not necessarily start and/or end at wells. This allows more efficient coverage and avoids the redundant work generally done in the near-well regions. We improved the accuracy of the streamline simulator with a higher order mapping from pressure grid to streamlines that significantly reduces smoothing errors, and a Kriging algorithm is used to map from the streamlines to the background grid. The higher accuracy of the Kriging mapping means that it is not essential for grid blocks to be crossed by one or more streamlines. The higher accuracy comes at the price of increased computational costs, but allows coarser coverage and so does not generally increase the overall costs of the computations. To reduce errors associated with fixing the pressure field between pressure updates, we developed a higher order global time-stepping method that allows the use of larger global time steps. Third-order ENO schemes are suggested to propagate components along streamlines. Both in the two-phase and three-phase experiments these ENO schemes outperform other (higher order) upwind schemes. Application of the third order ENO scheme leads to ii...

show abstract

“…Overall, the Flat scheme shows the least grid dependency. (Roe & Sidilkover, 1992), the CTU scheme (Collela, 1990) and Koren's scheme (Koren, 1991) Common Name (c) Koren'…”

Section: Experimentation and Discussionmentioning

confidence: 99%

Industrial Compositional Streamline Simulation for Efficient and Accurate Prediction of Gas Injection and WAG Processes

Gerritsen¹

2008

View full text Add to dashboard Cite

show abstract

“…First-order accuracy is, however, generally not sufficient for many applications, and second-order schemes are required for efficiency. These stable low-order smoothers have been used extensively with a higher-order operator via a defect correction scheme, which is identical to preconditioning, but is more amenable to a nonlinear solve (Atlas & Burrage (1994); Böhmer et al (1984); Dick (1991);Hemker (1986); Koren (1991)). …”

Section: Nonlinear Multigrid Methods For Mhdmentioning

confidence: 99%

“…Chacón (Chacón (2004;2008a;b)) reports on 2D tearing instability test cases and demonstrates a speedup ranging from 8 − 15 for a 128 2 mesh Chacón (2008a). Another example of a good verification test case in 3D is that of 3D island coalescence (Chacón (2008a)).…”

Section: Other Examplesmentioning

confidence: 99%

Implicit Numerical Methods for Magnetohydrodynamics

Samtaney¹

2012

Topics in Magnetohydrodynamics

View full text Add to dashboard Cite

“…is smaller. Moreover, in [9] it is shown that this scheme still allows a more efficient smoothing of point Gauss-Seidel relaxation than scheme (7). All this makes that it is a more appropriate candidate for our multigrid purposes than scheme (7).…”

Section: A Positive Continuously Differentiable Schemementioning

confidence: 94%

“…The present scheme is derived in [9]. (In another way and in another context, it is also derived in (10].…”

Section: A Positive Continuously Differentiable Schemementioning

confidence: 99%

Multi-D Upwinding and Multigridding for Steady Euler Flow Computations

Koren¹,

Hemker²

1992

Proceedings of the Ninth GAMM-Conference on Numerical Methods in Fluid Mechanics

View full text Add to dashboard Cite

Multi-dimensional upwind discretizations for the steady Euler equations are studied, with the emphasis on both a good accuracy and a good efficiency. The discretizations consist of a one-dimensional Riemann solver with locally rotated left and right cell face states, the rotation angle depending on the local flow solution. First, on the basis of a linear, scalar model equation, a study is made of the accuracy and stability properties of these schemes. Next the extension is made to the steady Euler equations. It is shown that for Euler flows, an appropriate local rotation angle can be found by maximizing a Riemann invariant along the middle subpath of the wave path in state space. For the steady1 two-dimensional Euler equations, numerical results are presented for some supersonic test cases with either oblique contact discontinuity or oblique shock wave.

show abstract

Low-Diffusion Rotated Upwind Schemes, Multigrid and Defect Correction for Steady, Multi-Dimensional Euler Flows

Cited by 12 publications

References 11 publications

Industrial Compositional Streamline Simulation for Efficient and Accurate Prediction of Gas Injection and WAG Processes

Industrial Compositional Streamline Simulation for Efficient and Accurate Prediction of Gas Injection and WAG Processes

Implicit Numerical Methods for Magnetohydrodynamics

Multi-D Upwinding and Multigridding for Steady Euler Flow Computations

Contact Info

Product

Resources

About