Differential equation based constrained reinitialization for level set methods

Hartmann, Daniel; Meinke, Matthias; Schröder, Wolfgang

doi:10.1016/j.jcp.2008.03.040

Cited by 88 publications

(108 citation statements)

References 18 publications

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“…For example, in a two-phase fluid problem with different fluid densities, this affects the mass conservation. Therefore, the recommended frequency with which this procedure should be applied depends on the application [16]. However, in our one-dimensional model, reinitialization does not affect the zero level set, but only the values of the level set function off the interface (since we always know the distance to the interface on the line).…”

Section: Level Set Methodsmentioning

confidence: 99%

Novel basin modelling concept for simulating deformation from mechanical compaction using level sets

et al. 2017

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As sedimentation progresses in the formation and evolution of a depositional geologic basin, the rock strata are subject to various stresses. With increasing lithostatic pressure, compressional forces act to compact the porous rock matrix, leading to overpressure buildup, changes in the fluid pore pressure and fluid flow. In the context of petroleum systems modelling, the present study concerns the geometry changes that a compacting basin experiences subject to deposition. The purpose is to track the positions of the rock layer interfaces as compaction occurs. To handle the challenge of potentially large geometry deformations, a new modelling concept is proposed that couples the pore pressure equation with a level set method to determine the movement of lithostratigraphic interfaces. The level set method propagates an interface according to a prescribed speed. The coupling term for the pore pressure and level-set equations consists of this speed function, which is dependent on the compaction law. The two primary features of this approach are the simplicity of the grid and the flexibility of the speed function. A first evaluation of the model concept is presented based on an implementation for one spatial dimension accounting for vertical effective stress. Isothermal conditions with a constant fluid density and viscosity were assumed. The accuracy of the implemented numerical solution for the case of a single stratigraphic unit with a linear compaction law was compared to the available analytical solution [38]. The multi-layer setup and the nonlinear case were tested for plausibility.

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Section: Level Set Methodsmentioning

confidence: 99%

Novel basin modelling concept for simulating deformation from mechanical compaction using level sets

et al. 2017

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“…Furthermore, the discretisation error in the transport appears as a loss of unit gradient for the distance function; as a result, the advection step is usually followed by re-initialisation. This can be done by direct calculation of distance [16] in a narrow band, or by solving an additional Eikonal equation to propagate the unit gradient constraint [17]. The best methods use implicit re-initialisation [12] or combine mass conservation properties of VOF and smoothness of LS in some way [11]; • Phase Field (PF) methods are developed on a basis that there exists a transport equation for self-similar advection of a tanh profile [18].…”

Section: Surface Capturing Modelsmentioning

confidence: 99%

CFD Analysis in Subsea and Marine Technology

Jasak

2017

IOP Conf. Ser.: Mater. Sci. Eng.

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Abstract. Computational Fluid Dynamics (CFD) is established in design and analysis for a range of industries, but its use in Marine and Naval Hydrodynamics is behind the trend. This can be attributed to the complexity of modelling needs, including presence of free surface, irregular transient flows, fluid-structure coupling and presence of established modelling tools based on potential theory.In this paper, state-of-the-art of CFD in Naval Hydrodynamics, wave and offshore applications is given, with an update of recent advances, validation and computing requirements for typical simulation cases. IntroductionSince the beginning of the 21st century, Computational Fluid Dynamics (CFD) has become well established across the range of engineering applications. CFD results are well understood, expectations on accuracy in design studies can be satisfied. For example, automotive industry uses CFD to significantly reduce the use of experimental studies in aerodynamics, internal combustion engine design and exhaust gas after-treatment. Indeed, CFD studies are now regularly performed in applications which were never properly analysed experimentally, such as passenger compartment comfort, vehicle soiling and acoustics-related phenomena, where the design primarily relies on CFD results.Acceptance of CFD in marine engineering, naval hydrodynamics and evaluation of wave loads appears to be lagging behind the trend of other industries. This is partially due to the complexity of free surface flows, but mainly by the fact that the phenomena under consideration imply significantly higher computational requirements. For example, sea-keeping studies of ships in irregular waves or calculation of transfer functions for wave loading on floating structures still cannot be performed at acceptable speed. "Engineering time-scale" in product design requires turn-over time of 8-12 hours for simulations to be practically useful.An important factor in the acceptance of CFD is the presence of alternative simulation tools. Numerical models based on potential flow theory are widely accepted, fast and validated and have been in use for more than a decade. The potential flow assumption, whole adequate for a part of industrial needs, brings it own limitations, mainly due to the formulation, or failure to account for coupled/non-linear effects. The best example is the evaluation of added resistance in waves, which may provide adequate loading results on the hull, but cannot account for forward speed of the ship.The challenges for CFD modelling in naval hydrodynamics can be grouped as follows:

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“…In both approaches, the second equation in (4) invokes a pseudo-time step that is different from the physical time step ( t) in the level-set equation. A first-order spatial discretization and forward Euler integration in the pseudo-time [19] is used here.…”

Section: The Sub-cell-fix Approachmentioning

confidence: 99%

“…To improve the stability and the accuracy of the sub-cell-fix method, Hartmann et al [19] recently proposed a hybrid of upwind and central difference schemes. Russo and Smereka's central scheme is replaced by an upwind discretization scheme across the zero level-set if the involving cells are not in the ; otherwise, central difference scheme is used to maintain high accuracy.…”

Section: The Sub-cell-fix Approachmentioning

confidence: 99%

See 1 more Smart Citation

Assessment and modification of sub‐cell‐fix method for re‐initialization of level‐set distance function

Sun

Wang

Bai

2009

Numerical Methods in Fluids

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SUMMARYSub-cell-fix re-initialization method was proposed by Russo and Smereka (J. Comput. Phys. 2000; 163: 51-67) as a modification to the re-distancing algorithm of Sussman et al. (J. Comput. Phys. 1994; 114: 146-159) that determines the distance function from an interface known as the zero level-set. The principal goal of sub-cell-fix method is to compute the distance function of the cells adjacent to the zero level-set without disturbing the original zero level-set. Following the original work of Russo and Smereka, several improved sub-cell-fix schemes were reported in the literature. In this paper, we show that in certain situations almost all the previous sub-cell-fix schemes can disturb the zero level-set, and the accuracy would not improve when the CFL numbers are decreased. Based on the scheme of Hartmann et al. (J. Comput. Phys. 2008; 227:6821-6845), we propose an improved sub-cell-fix scheme that can significantly increase the accuracy of sub-cell-fix method on problems that are challenging. The scheme makes use of a combination of the points adjacent to zero level-set surfaces and preserves the interface in a second-order accuracy. The new sub-cell-fix scheme is capable of handling large local curvature, and as a result it demonstrates satisfactory performance on several challenging test cases. Limitations of the schemes on highly stretched grids are illustrated.

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Differential equation based constrained reinitialization for level set methods

Cited by 88 publications

References 18 publications

Novel basin modelling concept for simulating deformation from mechanical compaction using level sets

Novel basin modelling concept for simulating deformation from mechanical compaction using level sets

CFD Analysis in Subsea and Marine Technology

Assessment and modification of sub‐cell‐fix method for re‐initialization of level‐set distance function

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