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25
Computational Physics Meets Computational Geometry
 State University of New York at Stony Brook
, 1996
"... Front Tracking is a methodology which uses computational geometry to provide numerical solutions of enhanced quality for problems of computational physics. It is particularly applicable to the computation of solutions with important jump discontinuities, or fronts. Fronts are represented as lower di ..."
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Front Tracking is a methodology which uses computational geometry to provide numerical solutions of enhanced quality for problems of computational physics. It is particularly applicable to the computation of solutions with important jump discontinuities, or fronts. Fronts are represented as lower dimensional data structures, which in the spirit of nonmanifold geometries used in CAD systems, support surfaces, curves (at surface intersections) and nodes (at common intersection points of three surfaces). These are expressed in the front tracking algorithm as a simplicial complex: data structures representing non intersecting smooth objects of given dimension, and boundary and coboundary operators to link them to lower and higher dimensional smooth objects. In the solution to problems of computational physics, these fronts evolve and can change their topology, forcing the need for fast retriangulation, intersection detection, and intersection removal routines. The methodology has been app...
A spacetime discontinuous Galerkin finite element method for twofluid problems
 Journal of Computational Physics
, 2006
"... A spacetime discontinuous Galerkin finite element method for two fluid flow problems is presented. By using a combination of level set and cutcell methods the interface between two fluids is tracked in spacetime. The movement of the interface in spacetime is calculated by solving the level set e ..."
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A spacetime discontinuous Galerkin finite element method for two fluid flow problems is presented. By using a combination of level set and cutcell methods the interface between two fluids is tracked in spacetime. The movement of the interface in spacetime is calculated by solving the level set equation, where the interface geometry is identified with the 0level set. To enhance the accuracy of the interface approximation the level set function is advected with the interface velocity, which for this purpose is extended into the domain. Close to the interface the mesh is locally refined in such a way that the 0level set coincides with a set of faces in the mesh. The two fluid flow equations are solved on this refined mesh. The procedure is repeated until both the mesh and the flow solution have converged to a reasonable accuracy. The method is tested on linear advection and Euler shock tube problems involving ideal gas and compressible bubbly magma. Oscillations around the interface are eliminated by choosing a suitable interface flux. Key words: cutcell method, discontinuous Galerkin finite element method, interface tracking, level set method, spacetime, two fluid flows. 1
Fully conservative leakproof treatment of thin solid structures immersed in compressible fluids
, 2012
"... ..."
Front Tracking: A Parallelized Approach for Internal Boundaries and Interfaces
 Applied Parallel Computing
, 1995
"... . Internal boundaries and interfaces are an important part of many fluid and solid modeling problems. Front Tracking contains a general interface framework, closely related to the nonmanifold geometry used in CAD solid modeling packages, to support numerical simulation of such fluid problems. It ca ..."
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. Internal boundaries and interfaces are an important part of many fluid and solid modeling problems. Front Tracking contains a general interface framework, closely related to the nonmanifold geometry used in CAD solid modeling packages, to support numerical simulation of such fluid problems. It can thus be considered to be a systematic application of the ideas of computational geometry to computational fluid dynamics. It is based on the principle that finite differences behave best when applied to differentiable functions, and that weak derivatives of nondifferentiable functions can be replaced by regularized expressions such as jump conditions. Front Tracking offers superior resolution for fluid problems with important discontinuities and interfaces, and in some cases, it has provided the unique method to obtain correct answers. Here we present Computer Science issues which have contributed to the success of Front Tracking: software design and organization  modularity, data struct...
A Hybrid Variational Front TrackingLevel Set Mesh Generator For Problems Exhibiting Large Deformations and Topological Changes
"... We present a method for generating 2D unstructured triangular meshes that undergo large deformations and topological changes in an automatic way. We employ a method for detecting when topological changes are imminent via distance functions and shape skeletons. When a change occurs, we use a level s ..."
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We present a method for generating 2D unstructured triangular meshes that undergo large deformations and topological changes in an automatic way. We employ a method for detecting when topological changes are imminent via distance functions and shape skeletons. When a change occurs, we use a level set method to guide the change of topology of the domain mesh. This is followed by an optimization procedure, using a variational formulation of active contours, that seeks to improve boundary mesh conformity to the zero level contour of the level set function. Our method is advantageous for ArbitraryLagrangianEulerian (ALE) type methods and directly allows for using a variational formulation of the physics being modeled and simulated, including the ability to account for important geometric information in the model (such as for surface tension driven flow). Furthermore, the meshing procedure is not required at every timestep and the level set update is only needed during a topological change. Hence, our method does not significantly affect computational cost. Key words:
On thin gaps between rigid bodies twoway coupled to incompressible flow
"... Twoway solid fluid coupling techniques typically calculate fluid pressure forces that in turn drive the solid motion. However, when solids are in close proximity (e.g. touching or in contact), the fluid in the thin gap region between the solids is difficult to resolve with a background fluid grid. ..."
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Twoway solid fluid coupling techniques typically calculate fluid pressure forces that in turn drive the solid motion. However, when solids are in close proximity (e.g. touching or in contact), the fluid in the thin gap region between the solids is difficult to resolve with a background fluid grid. Although one might attempt to address this difficulty using an adaptive, bodyfitted, or ALE fluid grid, the size of the fluid cells can shrink to zero as the bodies collide. The inability to apply pressure forces in a thin lubricated gap tends to make the solids stick together, since collision forces stop interpenetration but vanish when the solids are separating leaving the fluid pressure forces on the surface of the solid unbalanced in regards to the gap region. We address this problem by adding pressure degrees of freedom onto surfaces of rigid bodies, and subsequently using the resulting pressure forces to provide solid fluid coupling in the thin gap region. These pressure degrees of freedom readily resolve the tangential flow along the solid surface inside the gap and are twoway coupled to the pressure degrees of freedom on the grid allowing the fluid to freely flow into and out of the gap region. The twoway coupled system is formulated as a symmetric positivedefinite matrix which is solved using the preconditioned conjugate gradient method. Additionally, we provide a mechanism for advecting tangential velocities on solid surfaces in the gap region by extending semiLagrangian advection onto a curved surface mesh where a codimensionone velocity field tangential to the surface is defined. We demonstrate the convergence of our method on a number of examples, such as underwater rigid body separation and collision in both two and three spatial dimensions where typical methods do not converge. 1.
Toward Robust Front Tracking, Tracking Based on Conservation
"... Abstract: This work is aimed at developing front tracking methods based on conservation properties of ows for the one and two dimensional Euler systems of uid dynamics. The main idea of the work, which distinguishs the present methods from the traditioanl front tracking methods, is that they track d ..."
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Abstract: This work is aimed at developing front tracking methods based on conservation properties of ows for the one and two dimensional Euler systems of uid dynamics. The main idea of the work, which distinguishs the present methods from the traditioanl front tracking methods, is that they track discontinuities by enforcing the conservation properties in the numerical solutions. In doing this way, robustness are expected to be archieved for these tracking methods. Progresses and problems in this developement are discussed. Finally, numerical examples are presented to show the excellency of the methods. KeyWords: front tracking, robustness, enforcing conservation properties, cellaverage, discontinuity interaction. The PDE's under concern are Euler systems of hyperbolic equations in one and two space dimensions. As is well known, these systems describe the ows of nonviscous compressible uid; they embody the conservation of mass, momentum, and total energy. Our work is aimed at
A Front Tracking Method for RegularizationSensitive Shock Waves
, 1996
"... The regularizationsensitive waves, which often appear in nonstrictly hyperbolic and mixed elliptichyperbolic systems of conservation laws, are investigated. These weak solutions do not satisfy the Lax entropy criterion, and yet they are admissible under the viscous profile criterion; however th ..."
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The regularizationsensitive waves, which often appear in nonstrictly hyperbolic and mixed elliptichyperbolic systems of conservation laws, are investigated. These weak solutions do not satisfy the Lax entropy criterion, and yet they are admissible under the viscous profile criterion; however they are sensitively dependent on the parabolic regularization process. This sensitivity creates computational difficulties because of the artificial regularization, i.e., numerical diffusion, that is present in most numerical schemes. A new version of the fronttracking algorithm is developed to circumvent these difficulties. To propagate the discontinuous wave accurately, the iii algorithm utilizes a Riemann problem solver which directly accounts for the internal wave structure...
Archives of Computational Methods in Engineering State of the art reviews Numerical Simulation of TwoPhase Free Surface Flows
"... Free surface flows are of most interest in many engineering or mathematical problems and many methods have been developed for their numerical resolution in various fields of the physics or the engineering. In this work, the volumeoffluid method is used for the numerical simulation of twophase fre ..."
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Free surface flows are of most interest in many engineering or mathematical problems and many methods have been developed for their numerical resolution in various fields of the physics or the engineering. In this work, the volumeoffluid method is used for the numerical simulation of twophase free surface flows involving an incompressible liquid and a compressible gas and taking into account the surface tension effects. The incompressible NavierStokes equations are assumed to hold in the liquid domain, while the dynamical effects in the ideal gas are disregarded. A time splitting scheme is used together with a twogrids method for the space discretization. An original algorithm is introduced to track the bubbles of gas trapped in the liquid. Numerical results are presented in the frame of mold filling and bubbles and droplets flows. Some theoretical results concerning free boundary problems are also summarized. 1
DETAILED MODELLING OF FA AND DDT
"... The “state of the art” in numerical turbulent combustion modelling is a notion that strongly depends ..."
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The “state of the art” in numerical turbulent combustion modelling is a notion that strongly depends