The Characteristics-Based Matching (CBM) Method for Compressible Flow With Moving Boundaries and Interfaces

2004 ◽  
Vol 126 (4) ◽  
pp. 586-604 ◽  
Author(s):  
R. R. Nourgaliev ◽  
T. N. Dinh ◽  
T. G. Theofanous
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Level Set ◽  
Compressible Flows ◽  
Radical Change ◽  
Subsequent Paper ◽  
Ghost Fluid Method ◽  
Material Interface ◽  
Interface Position ◽  
Level Set Function

Recently, Eulerian methods for capturing interfaces in multi-fluid problems become increasingly popular. While these methods can effectively handle significant deformations of interface, the treatment of the boundary conditions in certain classes of compressible flows are known to produce nonphysical oscillations due to the radical change in equation of state across the material interface. One promising recent development to overcome these problems is the Ghost Fluid Method (GFM). The present study initiates a new methodology for boundary condition capturing in multifluid compressible flows. The method, named Characteristics-Based Matching (CBM), capitalizes on recent developments of the level set method and related techniques, i.e., PDE-based re-initialization and extrapolation, and the Ghost Fluid Method (GFM). Specifically, the CBM utilizes the level set function to capture interface position and a GFM-like strategy to tag computational nodes. In difference to the GFM method, which employs a boundary condition capturing in primitive variables, the CBM method implements boundary conditions based on a characteristic decomposition in the direction normal to the boundary. In this way overspecification of boundary conditions is avoided and we believe so will be spurious oscillations. In this paper, we treat (moving or stationary) fluid-solid interfaces and present numerical results for a select set of test cases. Extension to fluid-fluid interfaces will be presented in a subsequent paper.

The ‘Characteristics-Based Matching’ (CBM) Method for Compressible Flow With Moving Boundaries and Interfaces

2003 ◽  
Author(s):  
Robert Nourgaliev ◽  
Nam Dinh ◽  
Theo Theofanous
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Level Set ◽  
Compressible Flows ◽  
Moving Boundaries ◽  
Ghost Fluid Method ◽  
Material Interfaces ◽  
Interface Position ◽  
Level Set Function ◽  
Boundary Treatment

Recently, Eulerian methods for capturing interfaces in multi-fluid problems become increasingly popular. While these methods can effectively handle significant deformations of interface, they have been known to produce nonphysical oscillations near material interfaces due to the smeared out density profile and radical change in equation of state across a material interface. One promising recent development to overcome these problems is the ‘Ghost Fluid Method’ (GFM). While being able to produce excellent results for simulation of gas-gas flows, the GFM boundary treatment is unsatisfactory for the case of liquid-liquid or liquid-gas compressible flows. The present study devotes to a new methodology for boundary condition capturing in multi-fluid compressible flows. The method, named ‘Characteristics-Based Matching (CBM)’, capitalizes on the recent development of the level set method and related techniques, i.e., PDE-based re-initialization and extrapolation, and the ‘Ghost Fluid Method’ (GFM). Specifically, the CBM utilizes the level set function to ‘capture’ interface position and a GFM-like strategy to tag computational nodes. In difference to the GFM method, which employs a boundary condition capturing in primitive variables, the CBM method implements boundary conditions based on a characteristic decomposition in the direction normal to the boundary. Since the method allows to avoid over-specification of boundary conditions by respecting the information flow, we believe that the CBM is able to ‘cure’ above-mentioned problems of the GFM boundary condition capturing technique. In this paper, the method’s performance is examined on fluid dynamics problems with stationary and moving boundaries. Numerical results agree well with known analytical or computational solutions and experimental data. Robust and accurate solutions were obtained. In particular, spurious over/under-heating errors, typical for moving boundary treatment by other methods, are essentially eliminated in the CBM solutions.

On the Boundary Condition for the Level Set Function in the Numerical Simulation of Moving Contact Lines

2020 ◽  
Author(s):  
Pablo Gómez ◽  
Adolfo Esteban ◽  
Claudio Zanzi ◽  
Joaquín López ◽  
Julio Hernández
Keyword(s):  
Boundary Condition ◽  
Contact Angle ◽  
Level Set ◽  
Contact Line ◽  
Solid Wall ◽  
Interfacial Flows ◽  
Moving Contact ◽  
Level Set Function ◽  
Static Contact ◽  
Set Function

Abstract We present a method based on a level set formulation to reproduce the behavior of the contact line on solid walls in the simulation of 3D unsteady interfacial flows characterized by large density ratios. The level set method poses a particular difficulty, related to the reinitialization procedure, when used in the simulation of interfacial flows in which the interface intersects a solid wall, due to the appearance of a blind zone where standard reinitialization procedures produce inconsistent results. The proposed method overcomes this difficulty by introducing a boundary condition for the level set function on the solid surface based on the normal extension of the contact angle from the interface along the solid wall. In order to reproduce the dynamics of the contact line we use a simplified model that imposes a boundary condition on the interface curvature based on the static contact angle, and define a thin slip zone at the solid wall around the contact line. To assess the accuracy and robustness of the proposed method, we conducted several preliminary numerical tests in three dimensions, whose results are compared with analytical solutions and other results available in the literature.

Interface Tracking With a Coupled Level Set /VOF/Ghost Fluid Method: Application to Jet Atomization

2007 ◽  
Author(s):  
T. Me´nard ◽  
A. Berlemont
Keyword(s):  
Level Set ◽  
Stokes Equations ◽  
Level Set Methods ◽  
Mass Conservation ◽  
Navier Stokes ◽  
Interface Tracking ◽  
Ghost Fluid Method ◽  
Level Set Function ◽  
Wide Range ◽  
Break Up

We are here concerned by the primary break-up of a jet: a lot of topological changes occur and the Level Set Method thus appears well designed for our purpose. To describe the interface discontinuities, we use the Ghost Fluid Method (GFM) and a projection method is used to solve incompressible Navier-Stokes equations that are coupled to a transport equation for the level set function. The main drawback of level set methods is that numerical computations in the re-distancing algorithm can generate mass loss in under-resolved regions. To improve mass conservation extension of the method can be developed, namely a coupling between VOF and Level Set. In order to illustrate the abilities of the Level Set/VOF/Ghost Fluid method for interface tracking, we present a 3D simulation of the primary atomization zone of a turbulent liquid jet. The turbulence initiates some perturbations on the liquid surface, that are enhanced by the mean shear and break-up occurs. The generated liquid parcels show a wide range of shapes. Particular behaviors such ligament detachments, droplet formations and break up are described.

Reinitialization of the Level-Set Function in 3d Simulation of Moving Contact Lines

2016 ◽  
Vol 20 (5) ◽  
pp. 1163-1182 ◽  
Author(s):  
Shixin Xu ◽  
Weiqing Ren
Keyword(s):  
Boundary Condition ◽  
Contact Angle ◽  
Level Set ◽  
Contact Line ◽  
Dynamic Contact Angle ◽  
Coupled System ◽  
Dynamic Contact ◽  
Moving Contact ◽  
Level Set Function ◽  
Set Function

AbstractThe level set method is one of the most successful methods for the simulation of multi-phase flows. To keep the level set function close the signed distance function, the level set function is constantly reinitialized by solving a Hamilton-Jacobi type of equation during the simulation. When the fluid interface intersects with a solid wall, a moving contact line forms and the reinitialization of the level set function requires a boundary condition in certain regions on the wall. In this work, we propose to use the dynamic contact angle, which is extended from the contact line, as the boundary condition for the reinitialization of the level set function. The reinitialization equation and the equation for the normal extension of the dynamic contact angle form a coupled system and are solved simultaneously. The extension equation is solved on the wall and it provides the boundary condition for the reinitialization equation; the level set function provides the directions along which the contact angle is extended from the contact line. The coupled system is solved using the 3rd order TVD Runge-Kutta method and the Godunov scheme. The Godunov scheme automatically identifies the regions where the angle condition needs to be imposed. The numerical method is illustrated by examples in three dimensions.

Numerical Simulations of Shock-Bubble Interactions Using an Improved Ghost Fluid Method

2005 ◽  
Author(s):  
Hiroyuki Takahira ◽  
Shinya Yuasa
Keyword(s):  
Level Set Method ◽  
Level Set ◽  
Mass Conservation ◽  
Ghost Fluid Method ◽  
Hybrid Particle ◽  
Bubble Interactions ◽  
Level Set Function ◽  
Particle Level ◽  
Set Function ◽  
Particle Level Set Method

The present work is concerned with numerical simulations for the shock-bubble interactions using the Ghost Fluid Method (GFM) in which the interface is captured with level set methods. The GFM is applied to the interactions between an air shock wave and a cylindrical or spherical helium bubble to investigate the numerical diffusion in the reinitialization procedure of the level set function. It is shown that the interface is not captured accurately using the GFM without the reinitialization of the level set function. The numerical diffusion in the reinitialization procedure affects the formation of a re-entrant jet and vortex structures after a shock wave impacts the bubble. It is also shown that the results with the hybrid particle level set method agree with the experiments by Haas and Sturtevant. The hybrid particle level set method is superior in the mass conservation. Also, we have improved the GFM by correcting velocities, pressure and density at boundary nodes using the Riemann solutions to avoid numerical oscillations near the gas-liquid interface. We have succeeded in capturing the sharp interface for the shock-air bubble interaction in water by using the improved GFM coupling with the hybrid particle level set method. Mass conservation in the hybrid particle level set method is better than that in the standard level set method with high order discretization scheme.

An Adaptive, Finite Difference Solver for the Nonlinear Poisson-Boltzmann Equation with Applications to Biomolecular Computations

2013 ◽  
Vol 13 (1) ◽  
pp. 150-173 ◽  
Author(s):  
Mohammad Mirzadeh ◽  
Maxime Theillard ◽  
Asdís Helgadöttir ◽  
David Boy ◽  
Frédéric Gibou
Keyword(s):  
Boltzmann Equation ◽  
Finite Difference ◽  
Boundary Conditions ◽  
Level Set ◽  
Level Set Function ◽  
Novel Approach ◽  
Uniform Grids ◽  
Poisson Boltzmann ◽  
Finite Volume Approach ◽  
Poisson Boltzmann Equation

AbstractWe present a solver for the Poisson-Boltzmann equation and demonstrate its applicability for biomolecular electrostatics computation. The solver uses a level set framework to represent sharp, complex interfaces in a simple and robust manner. It also uses non-graded, adaptive octree grids which, in comparison to uniform grids, drastically decrease memory usage and runtime without sacrificing accuracy. The basic solver was introduced in earlier works [16,27], and here is extended to address biomolecular systems. First, a novel approach of calculating the solvent excluded and the solvent accessible surfaces is explained; this allows to accurately represent the location of the molecule’s surface. Next, a hybrid finite difference/finite volume approach is presented for discretizing the nonlinear Poisson-Boltzmann equation and enforcing the jump boundary conditions at the interface. Since the interface is implicitly represented by a level set function, imposing the jump boundary conditions is straightforward and efficient.

Sturm-Liouville Problem for Stationary Differential Operator with Nonlocal Two-Point Boundary Conditions

2006 ◽  
Vol 11 (1) ◽  
pp. 47-78 ◽  
Author(s):  
S. Pečiulytė ◽  
A. Štikonas
Keyword(s):  
Boundary Condition ◽  
Differential Operator ◽  
Boundary Conditions ◽  
Nonlocal Boundary Condition ◽  
Nonlocal Boundary ◽  
Liouville Problem ◽  
Complex Case ◽  
Qualitative Behavior ◽  
Point Boundary ◽  
Sturm Liouville

The Sturm-Liouville problem with various types of two-point boundary conditions is considered in this paper. In the first part of the paper, we investigate the Sturm-Liouville problem in three cases of nonlocal two-point boundary conditions. We prove general properties of the eigenfunctions and eigenvalues for such a problem in the complex case. In the second part, we investigate the case of real eigenvalues. It is analyzed how the spectrum of these problems depends on the boundary condition parameters. Qualitative behavior of all eigenvalues subject to the nonlocal boundary condition parameters is described.

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