parallel adaptive simplical re meshing for deforming domain cfd computations deforming domains occur in many fields of computational fluid dynamics cfd such as interface tracking simulation of pumps and engines and fluid structure interaction the deformation of the domain presents a challenge to the integrity of the computational mesh substantial motion of the domain boundaries requires vertex motion and changes in mesh connectivity for cases of simple boundary motion or structured meshes predetermined changes to the mesh structure can be sufficient however without a priori knowledge of how the domain will change a more robust solution is required the present work offers a parallelized solution for simplical meshes that is well suited to extremely complex geometry the mesh continuously evolves without user intervention or the use of target meshes varying length scales imposed by evolving boundary curvatures and narrow gaps are resolved with a fast length scale algorithm the set of algorithms are incorporated into an object oriented code structure that permits broad application to a range of cfd problems the robustness and versatility of the algorithm is demonstrated in several examples representing motion of internal and external boundaries where the boundary motion may or may not be known a priori

an algorithm for simplex tableau reduction the push to pull solution strategy the simplex algorithm requires artificial variables for solving linear programs which lack primal feasibility at the origin point we present a new general purpose solution algorithm called push to pull which obviates the use of artificial variables the algorithm consists of preliminaries for setting up the initialization followed by two main phases the push phase develops a basic variable set bvs which may or may not be feasible unlike simplex and dual simplex this approach starts with an incomplete bvs initially and then variables are brought into the basis one by one if the bvs is complete but the optimality condition is not satisfied then push phase pushes until this condition is satisfied using the rules similar to the ordinary simplex since the proposed strategic solution process pushes towards an optimal solution it may generate an infeasible bvs the pull phase pulls the solution back to feasibility using pivoting rules similar to the dual simplex method all phases use the usual gauss pivoting row operation and it is shown to terminate successfully or indicates unboundedness or infeasibility of the problem a computer implementation which further reduces the size of simplex tableau to the dimensions of the original decision variables is provided this enhances considerably the storage space and the computational complexity of the proposed solution algorithm illustrative numerical examples are also presented

control of an unstable reaction diffusion pde with long input delay abstract a smith predictor like design for compensation of arbitrarily long input delays is available for general controllable possibly unstable lti finite dimensional systems such a design has not been proposed previously for problems where the plant is a pde we present a design and stability analysis for a prototype problem where the plant is a reaction diffusion parabolic pde with boundary control the plant has an arbitrary number of unstable eigenvalues and arbitrarily long delay with an unbounded input operator the predictor based feedback design extends fairly routinely within the framework of infinite dimensional backstepping however the stability analysis contains interesting features that do not arise in predictor problems when the plant is an ode the unbounded character of the input operator requires that the stability be characterized in terms of the h 1 rather than the usual l 2 norm of the actuator state the analysis involves an interesting structure of interconnected pdes of parabolic and first order hyperbolic types where the feedback gain kernel for the undelayed problem becomes an initial condition in a pde arising in the compensator design for the problem with input delay space and time variables swap their roles in an interesting manner throughout the analysis

analysis of an exact fractional step method an exact fractional step or projection method for solving the incompressible navier stokes equations is analyzed the method is applied to both structured and unstructured staggered mesh schemes there are no splitting errors associated with the method it satisfies the incompressibility condition to machine precision and reduces the number of unknowns the exact projection technique is demonstrated on a two dimensional cavity flow and a multiply connected moving domain with a free surface its performance is compared directly to classic fractional step methods and shown to be roughly twice as efficient boundary conditions and the relationship of the method to streamfunction vorticity methods are discussed

finite time boundary stabilization of general linear hyperbolic balance laws via fredholm backstepping transformation this paper is devoted to a simple and new proof on the optimal finite control time for general linear coupled hyperbolic system by using boundary feedback on one side the feedback control law is designed by first using a volterra transformation of the second kind and then using an invertible fredholm transformation both existence and invertibility of the transformations are easily obtained

simulations of multiphase flows with multiple length scales using moving mesh interface tracking with adaptive meshing in multiphase flows the length scales of thin regions such as thin films between nearly touching drops and thin threads formed during the interface pinch off are usually several orders of magnitude smaller than the size of the drops in this paper a number of extra length criteria for adaptive meshes are developed and implemented in the moving mesh interface tracking method to solve these multiple length scale problems with high fidelity a nominal length scale based on the solutions of laplace s equations with the unit normal vectors of surfaces as the boundary conditions is proposed for the adaptive mesh refinement in the thin regions for almost flat interfaces boundaries which are near to the thin regions the averaged length of the interior edges sharing the two nodes with the boundary edge is introduced for the mesh adaptation the averaged length of the interfacial edges is used for the interior elements near the interfaces but outside of the thin regions for the interior mesh away from the interfaces boundaries different averaged length scales based on the initial mesh are employed for the adaptive mesh refining and coarsening numerous cases are simulated to demonstrate the capability of the proposed schemes in handling multiple length scales which include the relaxation and necking of an elongated droplet droplet droplet head on approaching droplet wall interactions and a droplet pair in a shear flow the smallest length resolved for the thin regions is three orders of magnitude smaller than the largest characteristic length of the problem

unsteady flow calculations with a parallel multiblock moving mesh algorithm a novel parallel dynamic moving mesh algorithm designed for multiblock parallel unsteady flow calculations using body fitted grids is presented the moving grid algorithm within each block uses a method of arc length based transfinite interpolation which is performed independently on local processors where the blocks reside a spring network approach is used to determine the motion of the corner points of the blocks which may be connected in an unstructured fashion in a general multiblock method a smoothing operator is applied to the points of the block face boundaries and edges to maintain grid smoothness and grid angles a multiblock parallel euler navier stokes solver using multigrid and dual time stepping is developed along with the moving mesh method computational results are presented for the unsteady flow calculations of airfoils and wings with deforming shapes as found in flutter simulations

tetrahedral mesh generation using delaunay refinement with non standard quality measures this paper studies the practical performance of delaunay refinement tetrahedral mesh generation algorithms by using non standard quality measures to drive refinement we show that sliver tetrahedra can be eliminated from constrained delaunay tetrahedralizations solely by refinement despite the fact that quality guarantees cannot be proven the algorithm can consistently generate meshes with dihedral angles between 18circ and 154 using a fairer quality measure targeting every type of bad tetrahedron dihedral angles between 14 and 154 can be obtained the number of vertices inserted to achieve quality meshes is comparable to that needed when driving refinement with the standard circumradius to shortest edge ratio we also study the use of mesh improvement techniques on delaunay refined meshes and observe that the minimum dihedral angle can generally be pushed above 20 regardless of the quality measure used to drive refinement the algorithm presented in this paper can accept geometric domains whose boundaries are piecewise smooth copyright 2011 john wiley sons ltd

finite element modelling of distribution problems a direct solution for the distribution problem is given being much more concise and efficient than those used at present it is then shown that with the constraint equations in the form used for this new method basis transformation can be applied to them to obtain a simple finite element network model of the optimal distribution problem more general fem network and continuum models are then discussed these having wide application in engineering and management science

modelling merging and fragmentation in multiphase flows with surfer we introduce a new numerical method called surfer for the simulation of two and three dimensional flows with several fluid phases and free interfaces between them we consider incompressible fluids obeying the navier stokes equation with newtonian viscosity in the bulk of each phase capillary forces are taken into account even when interfaces merge or break up fluid interfaces are advanced in time using an exactly volume conserving variant of the volume of fluid algorithm thus allowing for full symmetry between fluid phases the navier stokes equation is solved using staggered finite differences on a mac grid and a split explicit time differencing scheme while incompressibility is enforced using an iterative multigrid poisson solver capillary effects are represented as a stress tensor computed from gradients of the volume fraction function this formulation is completely independent of the topology of interfaces and relatively easy to implement in 3d it also allows exact momentum conservation in the discretized algorithm numerical spurious effects or parasite currents are noticed and compared to similar effects in boltzmann lattice gas methods for immiscible fluids simulations of droplets pairs colliding in 2d and in 3d are shown interface reconnection is performed easily despite the large value of capillary forces during reconnection

adaptive tetrahedral meshing in free surface flow an unstructured three dimensional moving mesh algorithm is developed for free surface flows with the capability of simulating large deformation a robust edge swapping algorithm and an optimization based mesh smoothing algorithm are used to improve mesh quality as the interface deforms the edge swapping algorithm uses an optimal swap sequence to transform configurations with several tetrahedra sharing a common edge the optimization based mesh smoothing relocates vertex position so that the minimum quality of the incident cells is maximized also edge contraction and bisection are used to adjust the mesh resolution according to surface curvature these local refinements effectively maintain good mesh quality and appropriate mesh size while avoiding global re meshing this scheme s robustness and accuracy are demonstrated with deforming liquid ligaments periodic jets and colliding droplets

minimum time output regulation for general linear heterodirectional hyperbolic systems this paper considers the minimum time output regulation problem for general linear heterodirectional hyperbolic systems with spatially varying coefficients for this a state feedback regulator ach

backstepping control of coupled linear parabolic pides with spatially varying coefficients this paper considers the backstepping design of state feedback controllers for coupled linear parabolic partial integro differential equations pides of volterra type with distinct diffusion coefficients spatially varying parameters and mixed boundary conditions the corresponding target system is a cascade of parabolic pdes with local couplings allowing a direct specification of the closed loop stability margin the determination of the state feedback controller leads to kernel equations which are a system of coupled linear second order hyperbolic pides with spatially varying coefficients and rather unusual boundary conditions by extending the method of successive approximations for the scalar case to the considered system class the well posedness of these kernel equations is verified by providing a constructive solution procedure this results in a systematic method for the backstepping control of coupled parabolic pides as well as pdes the applicability of the new backstepping design method is confirmed by the stabilization of two coupled parabolic pides with dirichlet robin unactuated boundaries and a coupled neumann actuation

construction of three dimensional improved quality triangulations using local transformations three dimensional delaunay triangulation are the most common form of three dimensional triangulation known but they are not very suitable for tetrahedral finite element meshes because they tend to contain poorly shaped sliver tetrahedra in this paper we present an algorithm for constructing improved quality triangulation with respect to a tetrahedron shape measure this algorithm uses combination of two or more local transformations to improve a given triangulation toward an optimal triangulation experimental results on finite element meshes show that this algorithm is much more effective than previous methods at removing slivers from delaunay triangulation and producing nearly optimal triangulation a variation of this algorithm for improving a pseudo locally optimal non delaunay triangulationn toward a delaunay triangulation is also presented

a two fluid spectral element method abstract a spectral element formulation for two fluid flows is presented which uses arbitrary lagrangian eulerian mesh movement with an unstructured mesh the main advantage of this approach is that the spectral elements provide a high order of accuracy while the unstructured mesh allows geometric flexibility the accuracy of this approach is demonstrated for several relatively simple configurations with and without moving interfaces another unique feature of the formulation as compared to previous single fluid spectral element methods is that a fully implicit time advancement scheme is used this is made possible by the development of a spectral multigrid iteration which solves the implicit governing equations in a fixed number of iterations insensitive to both the polynomial degree of the spectral elements and the number of elements in the mesh by using this approach solutions for both stiff unsteady problems and steady state problems can be obtained efficiently

analysis of moving mesh partial differential equations with spatial smoothing two moving mesh partial differential equations mmpdes with spatial smoothing are derived based upon the equidistribution principle this smoothing technique is motivated by the robust moving mesh method of dorfi and drury j comput phys 69 1987 pp 175 195 it is shown that under weak conditions the basic property of no node crossing is preserved by the spatial smoothing and a local quasi uniformity property of the coordinate transformations determined by these mmpdes is proven it is also shown that discretizing the mmpdes using centered finite differences these basic properties are preserved

an adaptive mesh algorithm for evolving surfaces simulation of drop breakup and coalescence abstract an algorithm is presented for the adaptive restructuring of meshes on evolving surfaces the resolution of the relevant local length scale is maintained everywhere with prescribed accuracy through the minimization of an appropriate mesh energy function by a sequence of local restructuring operations the resulting discretization depends on the instantaneous configuration of the surface but is insensitive to the deformation history application of the adaptive discretization algorithm is illustrated with three dimensional boundary integral simulations of deformable drops in stokes flow the results show that the algorithm can accurately resolve detailed features of deformed fluid interfaces including slender filaments associated with drop breakup and dimpled regions associated with drop coalescence our algorithm should be useful in a variety of fields including computational fluid dynamics image processing geographical information systems and biomedical engineering problems

primal mixed formulations for reaction diffusion systems on deforming domains we propose a finite element formulation for a coupled elasticity reaction diffusion system written in a fully lagrangian form and governing the spatio temporal interaction of species inside an elastic or hyper elastic body a primal weak formulation is the baseline model for the reaction diffusion system written in the deformed domain and a finite element method with piecewise linear approximations is employed for its spatial discretization on the other hand the strain is introduced as mixed variable in the equations of elastodynamics which in turn acts as coupling field needed to update the diffusion tensor of the modified reaction diffusion system written in a deformed domain the discrete mechanical problem yields a mixed finite element scheme based on row wise raviart thomas elements for stresses brezzi douglas marini elements for displacements and piecewise constant pressure approximations the application of the present framework in the study of several coupled biological systems on deforming geometries in two and three spatial dimensions is discussed and some illustrative examples are provided and extensively analyzed

fredholm backstepping control of coupled linear parabolic pdes with input and output delays this paper considers the observer based output feedback stabilization of coupled parabolic pdes with spatially varying coefficients and different diffusion coefficients subject to distinct constant input and output delays by representing the delays in the form of homodirectional hyperbolic systems a hyperbolic parabolic pde pde pde cascade is obtained the state feedback controller design for this system is based on a fredholm backstepping transformation mapping the closed loop system into a stable pde pde pde target system with this a minimum control time is achieved for the hyperbolic subsystem in the target dynamics then this approach is extended to the design of a state observer for delayed measurements to obtain an observer based output feedback controller exponential stability of the resulting closed loop system is verified furthermore it is shown that the fredholm and backstepping transformations related to the hyperbolic subsystems are attainable in closed form the new design procedure is demonstrated for the output feedback stabilization of two coupled parabolic pdes with different input and output delays

parallel scalable adjoint based adaptive solution of variable viscosity stokes flow problems we present a framework for parallel adaptive solution of variable viscosity stokes flow problems we focus on data structures algorithms and solvers that can scale to thousands of processor cores the problem is discretized by octree based finite elements with explicit enforcement of continuity constraints at hanging nodes the parallel octree structure allows for fast neighbor finding and facilitates local coarsening and refinement of the mesh mesh adaptivity is driven by a posteriori error indicators including adjoint based goal oriented techniques dynamic load balancing is achieved by dynamically partitioning a morton ordered space filling curve the stokes system is solved iteratively using the minimum residual method minres preconditioned by a schur complement based approximate inverse that employs algebraic multigrid v cycle approximations of the inverses of the poisson like operators we demonstrate the effectiveness of this framework on several testbed problems with up to 6 orders of magnitude variation in viscosity and up to 1 7 billion unknowns on up to 4096 cores the results indicate that the overhead due to all amr components is less than 3 of the overall solve time the solver exhibits very good algorithmic and parallel implementation scalability the solver is insensitive to the magnitude of viscosity variation and adjoint based adaptivity results in over two orders of magnitude reduction in number of unknowns and up to an order of magnitude improvement in runtime relative to a uniform mesh for the same level of error

an overset grid method for 3d unsteady incompressible flows a composite grid numerical method is developed for simulating unsteady three dimensional 3d incompressible flows in complex geometries the governing equations are solved using a second order accurate finite volume method based on the dual time stepping artificial compressibility approach overset grids are employed to discretize arbitrarily complex geometries and a new interface algorithm is developed to facilitate communication between neighboring grids the algorithm is inspired by the necessary and sufficient conditions for satisfying global mass conservation in a composite domain and is simple to implement in 3d numerical experiments show that the new interpolation scheme is superior to straightforward trilinear interpolation of all flow variables as it minimizes non physical spurious oscillations in the overlap region is less sensitive to grid refinement and greatly enhances the computational efficiency of the iterative algorithm the advantages of the new method are especially pronounced when adjacent overset subdomains are discretized with different spatial resolutions the potential of the method as a powerful technique for simulating complex engineering flows is demonstrated by applying it to calculate vortex shedding from a circular cylinder mounted between two endplates and flow in a rectangular channel with two wall mounted obstacles

a computer implementation of the push and pull algorithm and its computational comparison with lp simplex method the simplex algorithm requires artificial variables for solving linear programs which lack primal feasibility at the origin point we present a new general purpose solution algorithm called push and pull which obviates the use of artificial variables the algorithm consists of preliminaries for setting up the initialization followed by two main phases the push phase develops a basic variable set bvs which may or may not be feasible unlike simplex and dual simplex this approach starts with an incomplete bvs initially and then variables are brought into the basis one by one if the bvs is complete but the optimality condition is not satisfied then push phase pushes until this condition is satisfied using the rules similar to the ordinary simplex since the proposed strategic solution process pushes towards an optimal solution it may generate an infeasible bvs the pull phase pulls the solution back to feasibility using pivoting rules similar to the dual simplex method all phases use the usual gauss pivoting row operation and it is shown to terminate successfully or indicates unboundedness or infeasibility of the problem a computer implementation which enables the user to run either push and pull or ordinary simplex algorithms is provided the fully coded version of the algorithm is available from the authors upon request a comparison analysis to test the efficiency of push and pull algorithm comparing to ordinary simplex is accomplished illustrative numerical examples are also presented

boundary control of coupled reaction diffusion processes with constant parameters the problem of boundary stabilization is considered for some classes of coupled parabolic linear pdes of the reaction diffusion type with reference to n coupled equations each one equipped with a scalar boundary control input a state feedback law is designed with actuation at only one end of the domain and exponential stability of the closed loop system is proven the treatment is addressed separately for the case in which all processes have the same diffusivity and for the more challenging scenario where each process has its own diffusivity and a different solution approach has to be taken the backstepping method is used for controller design and particularly the kernel matrix of the transformation is derived in explicit form of series of bessel like matrix functions by using the method of successive approximations to solve the corresponding pde thus the proposed control laws become available in explicit form additionally the stabilization of an underactuated system of two coupled reaction diffusion processes is tackled under the restriction that only a scalar boundary input is available capabilities of the proposed synthesis and its effectiveness are supported by numerical studies made for three coupled systems with distinct diffusivity parameters and for underactuated linearized dimensionless temperature concentration dynamics of a tubular chemical reactor controlled through a boundary at low fluid superficial velocities when convection terms become negligible

output feedback stabilization of coupled reaction diffusion processes with constant parameters the problem of output feedback boundary stabilization is considered for n coupled plants distributed over the one dimensional spatial domain 0 1 where they are governed by linear reaction diffusion partial differential equations pdes all plants have constant parameters and each is equipped with its own scalar boundary control input acting at one end of the domain first a state feedback law is designed to exponentially stabilize the closed loop system with an arbitrarily fast convergence rate then collocated and anticollocated observers are designed using a single boundary measurement for each plant the exponential convergence of the observed state towards the actual one is demonstrated for both observers with a convergence rate that can be made as fast as desired finally the state feedback controller and the preselected either collocated or anticollocated observer are coupled together to yield an output feedback stabilizing controller the distinct treatments are proposed separately fo

transient adaptivity applied to two phase incompressible flows an anisotropic adaptation process is applied to a three dimensional incompressible two phase flow solver the solver uses a level set finite element method on unstructured tetrahedral meshes we show how the level set function can be used to build an anisotropic mesh with good properties some computations with a strong transient character and large densities ratios 1 1000 are presented we show that the efficiency of the computations can be deeply enhanced by mesh adaptations

an arbitrary lagrangian eulerian formulation for solving moving boundary problems with large displacements and rotations an arbitrary lagrangian eulerian ale formulation based on the unstructured finite volume method is proposed for solving moving boundary problems with large displacements and rotations the numerical method is based on the side centered arrangement of the primitive variables that does not require any ad hoc modifications in order to enhance pressure coupling the continuity equation is satisfied within each element at machine precision and the summation of the continuity equations can be exactly reduced to the domain boundary which is important for the global mass conservation a special attention is given to construct an ale algorithm obeying the discrete geometric conservation law dgcl the mesh deformation algorithm is based on the indirect radial basis function rbf algorithm at each time level while avoiding remeshing in order to enhance numerical robustness for the parallel solution of resulting large scale algebraic equations in a fully coupled form a matrix factorization is introduced similar to that of the projection method for the whole system and the parallel algebraic multigrid solver boomeramg is used for the scaled discrete laplacian provided by the hypre library which we access through the petsc library the present numerical algorithm is initially validated for the decaying taylor green vortex flow the flow past an oscillating circular cylinder in a channel and the flow induced by an oscillating sphere in a cubic cavity then the numerical algorithm is applied to the numerical simulation of flow field around a pair of flapping drosophila wings in hover flight the time variation of the eulerian coherent structures in the near wake is shown along with the aerodynamic loads

optimization of primal and dual network models of distribution abstract a direct one pass method of solution of the distribution problem is developed basis transformation is then applied to the original constraint equations of this to obtain a quadratic problem which can also be obtained by summation of finite element matrices in which the element constitutive parameter is respectively the route cost or inverse cost for the dual and primal problems using the method of steepest descent extrema for both these are obtained which are equal or close to the exact solutions

a high resolution characteristics based implicit dual time stepping vof method for free surface flow simulation on unstructured grids in this paper a new unstructured grid finite volume incompressible navier stokes solver based on a high order characteristics based method the artificial compressibility method and a matrix free implicit dual time stepping scheme has been developed to study unsteady free surface flows the free surface effects are calculated using the volume of fluid vof method and continuum surface force the transport equation for the vof is numerically solved using exactly the same method for the flow solver a number of test cases have been studied to validate the proposed method and demonstrate its capability by comparison with other schemes and published results

output regulation for coupled linear parabolic pides abstract this paper presents a backstepping based solution of the output regulation problem for coupled parabolic partial integro differential equations pides with spatially varying coefficients and distinct diffusion coefficients the considered setup assumes in domain as well as boundary disturbances while the output to be controlled can be defined distributed in domain pointwise in domain or at the boundaries and need not be measured by assuming a finite dimensional signal model which may also be non diagonalizable a systematic solution of the output regulation problem is presented by making use of observer based feedforward control existence conditions for the corresponding regulator are formulated in terms of the plant transfer behaviour for the resulting closed loop system exponential stability with a prescribed decay rate is verified the regulator design for two unstable coupled parabolic pides demonstrates the results of the paper

modeling merging and breakup in the moving mesh interface tracking method for multiphase flow simulations the three dimensional moving mesh interface tracking mmit method coupled with local mesh adaptations by quan and schmidt s p quan d p schmidt a moving mesh interface tracking method for 3d incompressible two phase flows j comput phys 221 2007 761 780 demonstrated the capability to accurately simulate multiphase flows to handle large deformation and also to perform interface pinch off for some specific cases however another challenge i e how to handle interface merging such as droplet coalescence has not been addressed in this paper we present a mesh combination scheme for interface connection and a more general mesh separation algorithm for interface breakup these two schemes are based on the conversion of liquid cells in one phase to another fluid by changing the fluid properties of the cells in the combination or separation region after the conversion the newly created interface is usually ragged and a local projection method is employed to smooth the interface extra mesh adaptation criteria are introduced to handle colliding interfaces with almost zero curvatures as the distance between the interfaces diminishes simulations of droplet pair collisions including both head on and off center coalescences show that the mesh adaptations are capable of resolving very small length scales and the mesh combination and mesh separation schemes can handle the topological transitions in multiphase flows the potential of our method to perform detailed investigations of droplet coalescence and breakup is also displayed

neumann boundary stabilization of one dimensional linear parabolic systems with input delay this paper addresses the boundary stabilization problem of one dimensional linear parabolic systems with input delay especially the case of neumann boundary control is studied the purpose is to derive the stabilizing controller of predictor type in a hilbert space by using a backstepping method combined with the semigroup theory the use of the semigroup theory makes the proof of continuity of the inverse transformation easy also it is shown that the implementation of the abstract controller is feasible by using a finite number of eigenvalues and eigenfunctions of the system operator

a continuum method for modeling surface tension abstract a new method for modeling surface tension effects on fluid motion has been developed interfaces between fluids of different properties or colors are represented as transition regions of finite thickness across which the color variable varies continuously at each point in the transition region a force density is defined which is proportional to the curvature of the surface of constant color at that point it is normalized so that the conventional description of surface tension on an interface is recovered when the ratio of local transition region thickness to local radius of curvature approaches zero the continuum method eliminates the need for interface reconstruction simplifies the calculation of surface tension enables accurate modeling of two and three dimensional fluid flows driven by surface forces and does not impose any modeling restrictions on the number complexity or dynamic evolution of fluid interfaces having surface tension computational results for two dimensional flows are given to illustrate the properties of the method

a front tracking method for the computations of multiphase flow direct numerical simulations of multiphase flows using a front tracking method are presented the method is based on writing one set of governing equations for the whole computational domain and treating the different phases as one fluid with variable material properties interfacial terms are accounted for by adding the appropriate sources as functions at the boundary separating the phases the unsteady navier stokes equations are solved by a conventional finite volume method on a fixed structured grid and the interface or front is tracked explicitly by connected marker points interfacial source terms such as surface tension are computed on the front and transferred to the fixed grid advection of fluid properties such as density is done by following the motion of the front the method has been implemented for fully three dimensional flows as well as for two dimensional and axisymmetric ones first the method is described for the flow of two or more isothermal phases the representation of the moving interface and its dynamic restructuring as well as the transfer of information between the moving front and the fixed grid are discussed applications and extensions of the method to homogeneous bubbly flows atomization flows with variable surface tension solidification and boiling are then presented

a hybrid particle level set method for improved interface capturing in this paper we propose a new numerical method for improving the mass conservation properties of the level set method when the interface is passively advected in a flow field our method uses lagrangian marker particles to rebuild the level set in regions which are underresolved this is often the case for flows undergoing stretching and tearing the overall method maintains a smooth geometrical description of the interface and the implementation simplicity characteristic of the level set method our method compares favorably with volume of fluid methods in the conservation of mass and purely lagrangian schemes for interface resolution the method is presented in three spatial dimensions