A variable relaxation scheme for multiphase, multicomponent flow

Krishnamurthy, Shalini; Gerritsen, Margot

doi:10.1007/s11242-007-9130-7

Cited by 3 publications

(15 citation statements)

References 33 publications

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“…Similarly, in compositional simulations, the coupling between components concentration and the phase behavior renders some problems more sensitive to numerical dispersion [14,15]. Examples of such problems include miscible and near miscible gas injection as well as surfactant flooding [16]. In this paper, we focus on low-salinity flooding and compositional gas injection.…”

Section: Numerical Dispersion Effects and Control In Multi-component mentioning

confidence: 99%

“…Among the tested schemes, a third order essentially non-oscillatory scheme was found the most the reliable and accurate [11]. Still, due to the nonlinearity of such systems, the application of higher-order schemes in three dimensions is nontrivial [11,16,31]. A key principle in the development of higher-order schemes involves the addition of anti-diffusion to cancel out truncation errors.…”

Section: Numerical Dispersion In Compositional Gas Simulationsmentioning

confidence: 99%

“…This anti-diffusion needs to be locally controlled such that it does not introduce spurious oscillations [14]. For compositional problems, due to the nonlinearity of the system, the determination of appropriate local antidiffusion levels requires characteristic decompositions, which are computationally very expensive [11,14,16].…”

Section: Numerical Dispersion In Compositional Gas Simulationsmentioning

confidence: 99%

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A segregated flow scheme to control numerical dispersion for multi-component flow simulations

AlSofi

Blunt

2012

Comput Geosci

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One of the challenges for reservoir simulation is numerical dispersion. For waterflooding applications the effect is controlled due to the self-sharpening nature of a Buckley-Leverett shock. However, for multicomponent flow simulations, incorrect wavespeeds can develop leading to the excessive smearing of fronts because of the coupling of compositional dispersion with the fractional flow. Rather than implementing a higher-order discretization method, we propose a simple scheme based on segregation-in-flow within a gridblock to control numerical dispersion. We extend the method originally proposed for polymer flooding to augmented waterflooding simulations in general as well as simulations of miscible or near miscible gas injection. For compositional simulations of gas injection, this is done through a coupled limited-flash/upstreamexclusion assumption. To test the scheme, an in-house streamline simulator has been modified and validated for modeling low-salinity floods as well as ternary two-phase displacements. Simulation results presented with and without segregation demonstrate the potential of the approach as a heuristic method to control numerical dispersion in multi-component flow simulations.

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Section: Numerical Dispersion Effects and Control In Multi-component mentioning

confidence: 99%

Section: Numerical Dispersion In Compositional Gas Simulationsmentioning

confidence: 99%

Section: Numerical Dispersion In Compositional Gas Simulationsmentioning

confidence: 99%

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A segregated flow scheme to control numerical dispersion for multi-component flow simulations

AlSofi

Blunt

2012

Comput Geosci

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“…These features make the relaxation method particularly suitable for those systems where the Riemann problem is difficult to solve or when it is not possible to perform analytical expression for Jacobians. The relaxation method is gradually applied to gas dynamics [14], shallow water motion [15], dynamic phase transition [16], multicomponent flow [17], magnetohydrodynamic [18].…”

Section: Introductionmentioning

confidence: 99%

A relaxation method for calculating detonation in condensed explosives

Yu¹,

Ma²

2014

Advances in Fluid Mechanics X

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Based on the relaxation approximation, the nonlinear governing equations of detonation in condensed explosives are transformed into linear relaxation systems, which can easily adopt simple and effective high resolution scheme. A fifth-order WENO reconstruction in space discretization and a fifth-order IMEX scheme of linear multistep methods with monotonicity and TVB in time discretization are utilized, where it can be avoid solving Riemann problem and calculating the Jacobian matrix of nonlinear flux, and it is not necessary to split the reaction source term. The present method is applied to simulate the steady structure of a one-dimensional planar detonation wave in condensed explosives, and the results demonstrate the excellent performance of the present method.

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“…One such example is the two-phase gas injection displacement in subsurface formations [31,11] which motivated this work and are discussed in detail in section 5.2. The governing systems of equations are characterized [21,11] by weak hyperbolicity at isolated points in space, strong nonlinear coupling, and flux evaluations that require computationally expensive thermal equilibrium calculations. Furthermore, Riemann solutions for these problems are available only for simplified phase behavior.…”

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confidence: 99%

Variable relaxed schemes for multidimensional hyperbolic conservation laws

Krishnamurthy¹,

Gerritsen²

2013

Preprint

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We present a new class of component-wise numerical schemes that are in the family of relaxation formulations, originally introduced by [S. Jin and Z. P. Xin, Comm. Pure Appl. Math., 48(1995), pp. 235-277]. The relaxation framework enables the construction of schemes that are free of nonlinear Riemann solvers and are independent of the underlying eigenstructure of the problem. The constant relaxation schemes proposed by Jin & Xin can however introduce strong numerical diffusion, especially when the maximum characteristic speeds are high compared to the average speeds in the domain. We propose a general class of variable relaxation formulations for multidimensional systems of conservation laws which utilizes estimates of local maximum and minimum speeds to arrive at more accurate relaxation schemes, irrespective of the contrast in maximum and average characteristic speeds. First and second order variable relaxation methods are presented for general nonlinear systems in one and two spatial dimensions, along with monotonicity and TVD (Total Variation Diminishing) properties for the 1D schemes. The effectiveness of the schemes is demonstrated on a test suite that includes Burgers' equation, the weakly hyperbolic Engquist-Runborg problem, as well as the weakly hyperbolic gas injection displacements that are governed by strong nonlinear coupling thus making them highly sensitive to numerical diffusion. In the latter examples the second order Jin-Xin scheme fails to capture the fronts reasonably, when both the first and second order variable relaxed schemes produce the displacement profiles sharply.

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A variable relaxation scheme for multiphase, multicomponent flow

Cited by 3 publications

References 33 publications

A segregated flow scheme to control numerical dispersion for multi-component flow simulations

A segregated flow scheme to control numerical dispersion for multi-component flow simulations

A relaxation method for calculating detonation in condensed explosives

Variable relaxed schemes for multidimensional hyperbolic conservation laws

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