consistent projection methods for variable density incompressible navier stokes equations with continuous surface forces on a rectangular collocated mesh two consistent projection methods of second order temporal and spatial accuracy have been developed on a rectangular collocated mesh for variable density navier stokes equations with a continuous surface force instead of the original projection methods denoted as algorithms i and ii in this paper in which the updated cell center velocity from the intermediate velocity and the pressure gradient is not guaranteed solenoidal the consistent projection methods denoted as algorithms iii and iv obtain the cell center velocity based on an interpolation from a conservative fluxes with velocity unit on surrounding cell faces dependent on treatment of the continuous surface force the pressure gradient in algorithm iii or the sum of the pressure gradient and the surface force in algorithm iv at a cell center is then conducted from the difference between the updated velocity and the intermediate velocity in a consistent projection method a non viscous 3d static drop with serials of density ratios is numerically simulated using the consistent projection methods the spurious currents can be greatly reduced and the pressure jump across the interface can be accurately captured without oscillations the developed consistent projection method are also applied for simulation of interface evolution of an initial ellipse driven by the surface tension and of an initial sphere bubble driven by the buoyancy with good accuracy and good resolution

higher order schemes with cip method and adaptive soroban grid towards mesh free scheme a new class of body fitted grid system that can keep the third order accuracy in time and space is proposed with the help of the cip constrained interpolation profile cubic interpolated propagation method the grid system consists of the straight lines and grid points moving along these lines like abacus soroban in japanese the length of each line and the number of grid points in each line can be different the cip scheme is suitable to this mesh system and the calculation of large cfl 10 at locally refined mesh is easily performed mesh generation and searching of upstream departure point are very simple and almost mesh free treatment is possible adaptive grid movement and local mesh refinement are demonstrated

a gradient augmented level set method for unstructured grids we present and test a gradient augmented level set method for unstructured grids which has been designed to allow for easy integration in parallel flow solvers the means to this end is a hermite formulation where the gradient is stored and advected as an independent variable along with the level set function the method uses narrow band storage in conjunction with a fast marching method which is also designed to take advantage of the gradient augmentation we demonstrate through standard passive advection test cases that the proposed method is able to compute interface motion with performance comparable to popular high performing methods on structured grids

sheaf theoretic investigation of cip method abstract the cip method is a numerical computational method in the computational fluid dynamics discovered by takewaki nishiguchi and yabe h takewaki a nishiguchi t yabe the cubic interpolated pseudo particle cip method for solving hyperbolic type equations j comput phys 61 1985 261 268 which shows nice properties as a numerical computational method but it is known that its mathematical essentials have not been revealed well in this article we investigate the cip method from an algebraic viewpoint then it is shown that the cip method is described well in terms of the sheaf theory

consideration of treatment of the boundary between different media in electromagnetic field analysis using the constrained interpolation profile method the treatment of a boundary between different media to simulate an electromagnetic em field is examined using the constrained interpolation profile cip method consideration of the way of handling spatial derivatives of fields is very important for cip em field analysis we demonstrate a method of handling this boundary and report results of cip em field analysis using the present approach

boundary fitted coordinate systems for numerical solution of partial differential equations a review a comprehensive review of methods of numerically generating curvilinear coordinate systems with coordinate lines coincident with all boundary segments is given some general mathematical framework and error analysis common to such coordinate systems is also included the general categories of generating systems are those based on conformal mapping orthogonal systems nearly orthogonal systems systems produced as the solution of elliptic and hyperbolic partial differential equations and systems generated algebraically by interpolation among the boundaries also covered are the control of coordinate line spacing by functions embedded in the partial differential operators of the generating system and by subsequent stretching transformation dynamically adaptive coordinate systems coupled with the physical solution and time dependent systems that follow moving boundaries are treated references reporting experience using such coordinate systems are reviewed as well as those covering the system development

applications of numerical conformal mapping abstract the application of conformal mapping methods to the solution of free surface flow problems is considered methods of numerical conformal mapping based on fourier series are extended to handle efficiently problems with time dependent boundaries they are shown to be practicable only for moderately distorted geometries extensions of the menikoff zemach method to breaking geometries are presented these latter methods are robust at quite large distortions but degrade prematurely in time dependent problems at amplitudes smaller than achieved by our recent vortex methods

effect of low boom waveform on focus boom using lossy nonlinear tricomi analysis focus boom occurs when a flight vehicle accelerates or maneuvers at supersonic speed its overpressure is typically more than three times greater than that of a cruise boom as a result future sup

three dimensional eulerian method for large deformation of viscoelastic fluid toward plate mantle simulation toward the unified simulation of the large deformation of a rigid viscoelastic material plate and the convection of a viscous fluid mantle an eulerian scheme with a semi lagrangian method is developed the scheme adopts the cip cslr method for advection terms of staggered grid system in three dimensions the positive transported profile of a positive quantity is assured by flux corrections in the dimensional splitting method the jaumann co rotational effect of the stress tensor is also integrated into the semi lagrangian treatment this co rotated semi lagrangian method is combined with an exponential time differencing method in the time development of the maxwell constitutive model the large time step comparable to or larger than the maxwell relaxation time is successfully realized validation tests are performed for the three dimensional rayleigh taylor instability of a viscoelastic material with jump discontinuity of the mass density and other material properties

global constraints for round robin tournament scheduling abstract in the presence of side constraints and optimization criteria round robin tournament problems are hard combinatorial problems commonly tackled with tree search and branch and bound optimization recent results indicate that constraint based tree search has crucial advantages over integer programming based tree search for this problem domain by exploiting global constraint propagation algorithms during search in this paper we analyze arc consistent propagation algorithms for the global constraints all different and one factor in the domain of round robin tournaments the best propagation algorithms allow us to compute all feasible perfectly mirrored pattern sets with minimal breaks for intermural tournaments of realistic size and to improve known lower bounds for intramural tournaments balanced with respect to carry over effects

kernel optimum nearly analytical discretization kond algorithm applied to parabolic and hyperbolic equations abstract two applications of the kernel optimum nearly analytical discretization kond algorithm to the parabolic and the hyperbolic type equations are presented in detail to lead to novel numerical schemes with very high numerical accuracy it is demonstrated numerically that the two dimensional kond p scheme for the parabolic type yields much less numerical error by over 2 3 orders measured quantitatively by the root mean square deviation from analytical solutions and reduces the cpu time to about 1 5 for a common numerical accuracy compared with the conventional explicit scheme of reference it is also demonstrated numerically that the kond h scheme for the hyperbolic type yields much less diffusive error and has fairly high stability for both of the linear and the nonlinear wave propagations compared with other conventional schemes origins of numerical errors in data processing in general numerical schemes are discussed

two numerical methods for the conformal mapping of simply connected domains abstract two numerical methods are considered for the conformai mapping of a bounded simply connected domain onto the unit disc the two methods are respectively the bergman kernel method which has been described in 17 and the so called ritz method in this paper we indicate the close theoretical relationship of the two methods compare their computational efficiencies and present a number of practical applications of the approximate conformal maps

a note on the basis set approach in the constrained interpolation profile method we propose a simple polynomial basis set that is easily extendable to any desired higher order accuracy this method is based on the constrained interpolation profile cip method and the profile is chosen so that the subgrid scale solution approaches the real solution by the constraints from the spatial derivative of the original equation by adopting the higher order derivatives of the master equations as constraints to generate a self consistent subgrid profile this solution quickly converges 3rd and 5th order polynomials are tested on the one dimensional schrodinger equation and are proved to give solutions a few orders of magnitude higher in accuracy than conventional methods for lowerlying eigenstates

a heuristic and evolutionary algorithm to optimize the coefficients of curve parametrizations parametric representations may have unnecessarily huge integer coefficients this can be a computational problem in practical applications in this paper we present an evolutionary algorithm that reduces the maximum length of the coefficients for a proper curve parametrization with integer coefficients this method is tested with different families of parametrizations and as we show the results are very satisfactory in terms of achievable quality and runtime consumption according to our knowledge this is the first algorithmic approach to this problem

a new directional splitting cip interpolation with high accuracy and low memory consumption a new directional splitting cip interpolation of third order accuracy is proposed this scheme uses only the value and first order derivatives of the physical field as computational variables and thus largely reduces the memory requirement the higher order cross derivatives are not treated as the computational variables but calculated by recursively using the local taylor expansions within each single mesh cell which retains the third order accuracy even for meshes of non uniform grid spacings the proposed directional splitting can be easily extended to solve advection equations of any multi dimensionality

exactly conservative semi lagrangian scheme for multi dimensional hyperbolic equations with directional splitting technique abstract a new numerical method that guarantees exact mass conservation is proposed to solve multidimensional hyperbolic equations in semi lagrangian form the method is based on the constrained interpolation profile cip scheme and keeps the many good characteristics of the original cip scheme the cip strategy is applied to the integral form of variables although the advection and nonadvection terms are separately treated mass conservation is kept in the form of a spatial profile inside a grid cell therefore it retains various advantages of the semi lagrangian solution with exact conservation which has been beyond the capability of conventional semi lagrangian schemes

a gradient augmented level set method with an optimally local coherent advection scheme the level set approach represents surfaces implicitly and advects them by evolving a level set function which is numerically defined on an eulerian grid here we present an approach that augments the level set function values by gradient information and evolves both quantities in a fully coupled fashion this maintains the coherence between function values and derivatives while exploiting the extra information carried by the derivatives the method is of comparable quality to weno schemes but with optimally local stencils performing updates in time by using information from only a single adjacent grid cell in addition structures smaller than the grid size can be located and tracked and the extra derivative information can be employed to obtain simple and accurate approximations to the curvature we analyze the accuracy and the stability of the new scheme and perform benchmark tests

advecting normal vectors a new method for calculating interface normals and curvatures when modeling two phase flows in simulating two phase flows interface normal vectors and curvatures are needed for modeling surface tension in the traditional approach these quantities are calculated from the spatial derivatives of a scalar function e g the volume of fluid or the level set function at any instant in time the orders of accuracy of normals and curvatures calculated from these functions are studied a new method for calculating these quantities is then presented where the interface unit normals are advected along with whatever function represents the interface and curvatures are calculated directly from these advected normals to illustrate this new approach the volume of fluid method is used to represent the interface and the advected normals are used for interface reconstruction the accuracy and performance of the new method are demonstrated via test cases with prescribed velocity fields the results are compared with those of traditional approaches

scheduling double round robin tournaments with divisional play using constraint programming abstract we study a tournament format that extends a traditional double round robin format with divisional single round robin tournaments elitserien the top swedish handball league uses such a format for its league schedule we present a constraint programming model that characterizes the general double round robin plus divisional single round robin format this integrated model allows scheduling to be performed in a single step as opposed to common multistep approaches that decompose scheduling into smaller problems and possibly miss optimal solutions in addition to general constraints we introduce elitserien specific requirements for its tournament these general and league specific constraints allow us to identify implicit and symmetry breaking properties that reduce the time to solution from hours to seconds a scalability study of the number of teams shows that our approach is reasonably fast for even larger league sizes the experimental evaluation of the integrated approach takes considerably less computational effort to schedule elitserien than does the previous decomposed approach

the cubic interpolated pseudo particle cip method application to nonlinear and multi dimensional hyperbolic equations abstract the basic of cip as a method to solve hyperbolic equations is re examined from a different viewpoint and the scheme is modified into an explicit finite difeerence form the method gives a stable and less diffusive result for square wave propagation compared with fct and a better result for propagation of a sine wave with a discontinuit the scheme is extended to nonlinear and multi dimensional problems

analysis of an electromagnetic field created by line current using constrained interpolation profile method development of accurate schemes is a technical issue related to calculation of electromagnetic fields this study uses constrained interpolation profile cip method to analyze electromagnetic fields created by line current this is a novel method proposed by yabe comparison of results obtained using finite difference time domain fdtd analysis and cip analysis indicates that cip analysis provides higher accuracy using identical discretization in addition given the same level of accuracy cip analysis requires less memory and less calculation time

a benders approach for the constrained minimum break problem this paper presents a hybrid ip cp algorithm for designing a double round robin schedule with a minimal number of breaks both mirrored and non mirrored schedules with and without place constraints are considered the algorithm uses benders cuts to obtain feasible home away pattern sets in few iterations and this approach leads to significant reductions in computation time for hard instances furthermore the algorithm is capable of solving a number of previously unsolved benchmark problems for the traveling tournament problem with constant distances

conformal mappings for internal viscous flow problems abstract isolated occlusions in a straight channel or pipe can be described analytically in a fashion that allows efficient accurate computation of nonlinear flow fields through conformal transformations

a region based quantum evolutionary algorithm rqea for global numerical optimization this work presents the region based quantum evolutionary algorithm rqea for solving numerical optimization problems in the proposed algorithm the feasible solution space is decomposed into regions in terms of quantum representation as the search progresses from one generation to the next the quantum bits evolve gradually increasing the probability of selecting regions that yield good fitness values through the inherent probabilistic mechanism the rqea initially behaves as a global search algorithm and gradually evolves into a local search algorithm resulting in a good balance between exploration and exploitation the rqea is applied to a series of numerical optimization problems the experiments show that the results obtained by the rqea are better than those obtained using state of the art qea and deahcspx

the use of splines and singular functions in an integral equation method for conformal mapping we consider the integral equation method of symm for the conformal mapping of simply connected domains for the numerical solution we examine the use of spline functions of various degrees for the approximation of the source density in particular we consider ways for overcoming the difficulties associated with corner singularities for this we modify the spline approximation and in the neighborhood of each corner where a boundary singularity occurs we approximate by a function which reflects the main singular behaviour of the source density the singular functions are then blended with the splines which approximate on the remainder of the boundary so that the global approximating function has continuity of appropriate order at the transition points between the two types of approximation we show by means of numerical examples that such approximations overcome the difficulties associated with corner singularities and lead to numerical results of high accuracy

high order zip differencing of convective terms the zip flux form for differencing the term wv x where w is a convected quantity and v is a convective velocity is observed to be equivalent to differencing the alternative expression wvx wxv using centered second order finite differences the advantage of this form is that one class of nonlinear computational instabilities is eliminated based on this observation the extension of the zip flux concept to arbitrarily high order accuracy is given computational examples show the advantage both of the zip flux concept itself and of its higher order forms within the context of flux corrected transport fct algorithms

cubic interpolated pseudo particle method cip for solving hyperbolic type equations abstract a new cubic polynomial interpolation method where the gradient of the quantity is a free parameter is proposed for solving hyperbolic type equations various choices of the gradient are investigated and a stable and less diffusive scheme is made possible without the clipping or the flux correction procedure

short note a simple and conservative operator splitting semi lagrangian volume of fluid advection scheme a semi lagrangian operator splitting high performance volume of fluid advection scheme slosh vof is developed in the backward time integration a directional splitting strategy is adopted which greatly simplifies the definition and locating of the departure volume and reduces it to a grid cell expanded or compressed in one grid direction the vof value in the departure cell is estimated using a geometrical interpolation algorithm with a piecewise linear interface calculation plic scheme for the interfacial cells the proposed slosh vof method is unconditionally stable and very large time steps can be used to significantly speed up the overall computations it is conceptually simple and can be very easily implemented due to the direction split advection its performance is evaluated through several benchmark advection tests the slosh vof results are comparable to those from an eulerian vof method in terms of interface position errors and improved with regard to mass conservation even with cfl numbers increased up to one order of magnitude

de eda a new evolutionary algorithm for global optimization differential evolution de was very successful in solving the global continuous optimization problem it mainly uses the distance and direction information from the current population to guide its further search estimation of distribution algorithm eda samples new solutions from a probability model which characterizes the distribution of promising solutions this paper proposes a combination of de and eda de eda for the global continuous optimization problem de eda combines global information extracted by eda with differential information obtained by de to create promising solutions de eda has been compared with the best version of the de algorithm and an eda on several commonly utilized test problems experimental results demonstrate that de eda outperforms the de algorithm and the eda the effect of the parameters of de eda to its performance is investigated experimentally

the application of shape preserving splines for the solution of differential equations this paper investigates the use of shape preserving interpolants based on bernstein polynomials for the numerical solution of differential equations a simple and accurate algorithm is presented for the integration of the initial value ordinary differential equation as well as for the partial differential equation of the burger type