short note a new minimum storage runge kutta scheme for computational acoustics a new fourth order six stage runge kutta numerical integrator that requires 2n storage n is the number of degrees of freedom of the system with low dissipation and dispersion and a relatively large stability interval is proposed these features make it a suitable time advancing method for solving wave propagation problems in computational acoustics some numerical experiments are presented to show the favourable behaviour of the new scheme as compared with the ldd46 and ldd25 methods proposed by stanescu and habashi j comput phys 143 1998 674 and the standard fourth order runge kutta method

the numerical analysis of ordinary differential equations runge kutta and general linear methods mathematical and computational introduction the euler method and its generalizations analysis of runge kutta methods general linear methods bibliography

application of a nonlinear computational aeroacoustics code to the gust airfoil problem a time domain solution of the gust airfoil problem is obtained using a high accuracy computational aeroacoustics code to solve the nonlinear euler equations for computational efficiency the equations are cast in chain rule curvilinear form and a structured multiblock solver is used on a distributed memory parallel computer cluster to fully investigate the performance of this solver a test matrix of benchmark problems is computed two airfoil geometries and four gust reduced frequencies these results are compared to benchmark solutions both on the airfoil surface and in the flow domain

on some new low storage implementations of time advancing runge kutta methods in this paper explicit runge kutta rk schemes with minimum storage requirements for systems with very large dimension that arise in the spatial discretization of some partial differential equations are considered a complete study of all four stage fourth order schemes of the minimum storage families of williamson 1980 2 van der houwen 1977 8 and ketcheson 2010 12 that require only two storage locations per variable is carried out it is found that whereas there exist no schemes of this type in the williamson and van der houwen families there are two isolated schemes and a one parameter family of fourth order schemes in four stage ketcheson s family this available parameter is used to obtain the optimal scheme taking into account the 2 norm of the coefficients of the leading error term in addition a new alternative minimum storage family to the s stage ketcheson that depends also on 3 s 3 free parameters is proposed this family contains both the williamson and van der houwen schemes but it is not included in ketcheson s family finally the results of some numerical experiments are presented to show the behavior of fourth order optimal schemes for some nonlinear problems

solution of the system of ordinary differential equations by adomian decomposition method in this article we use adomian decomposition method which is a well known method for solving functional equations now a days to solve systems of differential equations of the first order and an ordinary differential equation of any order by converting it into a system of differential of the order one theoretical considerations are being discussed and convergence of the method for theses systems is addressed some examples are presented to show the ability of the method for linear and non linear systems of differential equations

multidimensional optimization of finite difference schemes for computational aeroacoustics because of the long propagation distances computational aeroacoustics schemes must propagate the waves at the correct wave speeds and lower the isotropy error as much as possible the spatial differencing schemes are most frequently analyzed and optimized for one dimensional test cases therefore in multidimensional problems such optimized schemes may not have isotropic behavior in this work optimized finite difference schemes for multidimensional computational aeroacoustics are derived which are designed to have improved isotropy compared to existing schemes the derivation is performed based on both taylor series expansion and fourier analysis various explicit centered finite difference schemes and the associated boundary stencils have been derived and analyzed the isotropy corrector factor a parameter of the schemes can be determined by minimizing the integrated error between the phase or group velocities on different spatial directions the order of accuracy of the optimized schemes is the same as that of the classical schemes the advantage being in reducing the isotropy error the present schemes are restricted to equally spaced cartesian grids so the generalized curvilinear transformation method and cartesian grid methods are good candidates the optimized schemes are tested by solving various multidimensional problems of aeroacoustics

positive solutions for schrodinger poisson equations with a critical exponent abstract in this paper we establish the existence of a positive solution of the schrodinger poisson equations with a critical sobolev exponent the methods used here are based on the concentration compactness principle of p l lions and methods of brezis and nirenberg

cfl conditions for runge kutta discontinuous galerkin methods on triangular grids we study time step restrictions due to linear stability constraints of runge kutta discontinuous galerkin methods on triangular grids the scalar advection equation is discretized in space by the discontinuous galerkin method with either the lax friedrichs flux or the upwind flux and integrated in time with various runge kutta schemes designed for linear wave propagation problems or non linear applications von neumann like analyses are performed on structured periodic grids made up of congruent elements to investigate the influence of element shape on the stability restrictions we assess cfl conditions based on different element size measures among which only the radius of the inscribed circle and the shortest height prove appropriate although they are not totally independent of the triangle shape we explain their general behaviour with respect to element quality and report the corresponding courant numbers with both types of flux and polynomial order p ranging from 1 to 10 for use as guidelines in practical simulations we also compare the performance of the lax friedrichs flux and the upwind flux and we draw general conclusions about the relative computational efficiency of rk schemes the application of cfl conditions to two examples involving respectively an unstructured and a hybrid grid confirms our results although it shows that local stability criteria tend to yield too restrictive conditions

high accuracy large step explicit runge kutta hale rk schemes for computational aeroacoustics in many realistic calculations the computational grid spacing required to resolve the mean flow gradients is much smaller than the grid spacing required to resolve the unsteady propagating waves of interest because of this the high temporal resolution provided by existing optimized time marching schemes can be excessive due to the small time step required for stability in regions of clustered grid in this work explicit fourth order accurate runge kutta time marching schemes are optimized to increase the inviscid stability limit rather than the accuracy at large time steps single and multiple step optimized schemes are developed and analyzed the resulting schemes are validated on several realistic benchmark problems

wavenumber optimized immersed boundary method for aeroacoustic analysis based on cartesian mesh an immersed boundary method ibm suitable for aeroacoustic analysis is developed using the block structured cartesian mesh method called the building cube method the ibm using a ghost cell approach in conjunction with an image point is employed a hybrid interpolation scheme combining the wavenumber based method and inverse distance weighting method is introduced to the ibm this method is evaluated using four test cases the results of interpolation at an image point indicate that the wavenumber based method provides more accurate results than standard interpolation methods for aeroacoustic problems the results of acoustic scattering around a sphere show that the proposed ibm achieves better than second order accuracy in the case of noise propagation from a generic inlet the proposed ibm is shown to yield more accurate predictions for the far field sound pressure level than the inverse distance weighting based ibm in a different application involving the jt15d nacelle the far field sound pressure

infinitely many solutions of a symmetric dirichlet problem here q is a bounded domain in r with smooth boundary and f i r is c and satisfies certain growth conditions if m 1 and f is an even function hence f r r is an odd function then ambrosetti and rabinowitz l 21 proved the existence of infinitely many weak solutions of d using a symmetric version of the mountain pass theorem a similar result is due to michalek 3 who considered the case where m 21 rm s c and f is invariant under a free action of the cyclic group z p on c here z p is considered as a subgroup of s c c acting essentially via scalar multiplication on c in this paper we want to investigate which kind of symmetries guarantee the existence of infinitely many solutions of d let g be a compact lie group and p g o m an orthogonal representation of g on lrm then g acts on irm via the map g x ir ir g u y gv p g v we write v for the space rm considered as a g space do there exist infinitely many solutions of d if f is invariant under this symmetry i e f gu f u for all g e g and u e v without further assumptions on p the answer to this question is no in general for example if p g id for all g e g then there is no symmetry at all and one cannot expect infinitely many solutions more generally one should exclude the existence of fixed points vg u e vi gu u for all g e g 0 our first result says that there exist infinitely many solutions of d if the following condition is satisfied

existence of infinitely many large solutions for the nonlinear schrodinger maxwell equations abstract in this paper we study the nonlinear stationary schrodinger maxwell equations u v x u u f x u in r 3 u 2 in r 3 using the variant fountain theorem introduced by zou w zou variant fountain theorems and their applications manuscripta math 104 2001 343 358 under certain assumptions on v and f we get infinitely many large solutions for

multiple solutions for a nonlinear schrodinger poisson system with sign changing potential this paper deals with the existence and multiplicity of nontrivial solutions for a nonlinear schrodinger poisson system under some suitable conditions some criteria on the existence of nontrivial solutions including a ground state solution two solutions and a sequence of nontrivial solutions u k with u k 0 as k is established by applying the morse theory and variational methods some known results in the literatures are extended and improved

high energy solutions for the superlinear schrodinger maxwell equations abstract in this paper we study the existence of infinitely many large energy solutions for the superlinear schrodinger maxwell equations u v x u u f x u in r 3 u 2 in r 3 via the fountain theorem in critical point theory

on ground state solutions for the schrodinger poisson equations with critical growth abstract in this paper we study the existence of ground state solutions for the following schrodinger poisson equation u v x u u u q 1 u u 4 u in r 3 u 2 in r 3 where is a positive parameter under some certain assumptions on v we prove that for every 0 and q 2 5 such a class of schrodinger poisson equation with critical growth has at least a positive ground state solution via variational methods some recent results from the literature are extended

the importance of the unsteady kutta condition when modelling gust aerofoil interaction abstract the kutta condition is applied to aerofoils with sharp trailing edges to allow for viscous effects to be considered within a simplified system of equations that are inviscid this paper discusses in detail the inclusion of an unsteady kutta condition at a sharp trailing edge during gust aerofoil interaction and illustrates how the analytic solution for the far field noise generated by this interaction changes if the unsteady kutta condition is neglected or more precisely if the unsteady pressure is permitted to be singular at the trailing edge the analytic solution both with and without the unsteady kutta condition is compared with numerical results that have no imposed unsteady kutta condition importantly the results agree well only when the unsteady kutta condition is neglected in the analytic solution this paper highlights where the far field acoustics are most affected by neglecting the unsteady kutta condition for a variety of singularities that can occur in the unsteady pressure at the trailing edge and shows that results permitting different behaviour in the unsteady surface pressure at the trailing edge could give significantly different far field noise predictions even though the surface pressure elsewhere along the aerofoil surface agrees with benchmark solutions

efficient low storage runge kutta schemes with optimized stability regions a variety of numerical calculations especially when considering wave propagation are based on the method of lines where time dependent partial differential equations pdes are first discretized in space for the remaining time integration low storage runge kutta schemes are particularly popular due to their efficiency and their reduced memory requirements in this work we present a numerical approach to generate new low storage runge kutta lsrk schemes with optimized stability regions for advection dominated problems adapted to the spectral shape of a given physical problem those methods are found to yield significant performance improvements over previously known lsrk schemes as a concrete example we present time domain calculations of maxwell s equations in fully three dimensional systems discretized by a discontinuous galerkin approach

numerical simulation of separation control for transitional highly loaded low pressure turbines the subsonic flow through highly loaded low pressure turbines is simulated numerically using a high order method the configuration approximates cascade experiments that were conducted to investigate a reduction in turbine stage blade count which can decrease both weight and mechanical complexity at a nominal reynolds number of 25 10 3 based upon axial chord and inlet conditions massive separation occurs on the suction surface of each blade as a result of uncovered turning pulsed injection vortex generator jets were then used to help mitigate separation thereby reducing wake losses computations were performed for both uncontrolled and controlled cases and reproduced the transitional flow occurring in the aft blade and near wake regions the numerical method utilizes a centered compact finite difference scheme to represent spatial derivatives which is used in conjunction with a low pass pade type nondispersive filter operator to maintain stability an implicit approximately factored time marching algorithm is employed and newton like subiterations are applied to achieve second order temporal accuracy calculations were carried out on a massively parallel computing platform using domain decomposition to distribute subzones on individual processors a high order overset grid approach preserved spatial accuracy in locally refined embedded regions features of the flowfields are elucidated and simulations are compared with each other and with available experimental data relative to the uncontrolled case it was found that pulsed injection maintained attached flow over an additional 15 of the blade chord resulting in a 22 decrease of the wake total pressure loss coefficient

optimized compact finite difference schemes with maximum resolution direct numerical simulations and computational aeroacoustics require an accurate finite difference scheme that has a high order of truncation and high resolution characteristics in the evaluation of spatial derivatives compact finite difference schemes are optimized to obtain maximum resolution characteristics in space for various spatial truncation orders an analytic method with a systematic procedure to achieve maximum resolution characteristics is devised for multidiagonal schemes based on the idea of the minimization of dispersive phase errors in the wave number domain and these are applied to the analytic optimization of multidiagonal compact schemes actual performances of the optimized compact schemes with a variety of truncation orders are compared by means of numerical simulations of simple wave convections and in this way the most effective compact schemes are found for tridiagonal and pentadiagonal cases respectively from these comparisons the usefulness of an optimized high order tridiagonal compact scheme that is more efficient than a pentadiagonal scheme is discussed for the optimized high order spatial schemes the feasibility of using classical high order runge kutta time advancing methods is investigated

existence of positive solutions to the schrodinger poisson system without compactness conditions abstract in this paper we discuss the existence of a positive radial solution to a generalized schrodinger poisson system without compactness conditions by the method of the combination of a cut off function a monotonicity trick and a pohozaev type identity we obtain the boundedness of a palais smale sequence

multiplicity of small negative energy solutions for a class of nonlinear schrodinger poisson systems this paper deals with the following nonlinear schrodinger poisson email protected v x u k x f x u h x f x u inr 3 email protected f k x u 2 inr 3 where v x k x and h x are nonnegative continuous functions under appropriate assumptions on v x k x h x and f x u we prove the existence of infinitely many small negative energy solutions by using the variant fountain theorem established by zou recent results from the literature are extended

infinitely many solutions for schrodinger maxwell equations with indefinite sign subquadratic potentials in this paper we deal with multiplicity of solutions of a class of sublinear schrodinger maxwell equations du v x u fu f x u inr 3 d f u 2 lim x f x 0 inr 3 under more relaxed assumptions on v and f we establish some existence criteria to guarantee that the above problem has at least one or infinitely many nontrivial solutions by using the genus properties in critical theory

optimal runge kutta schemes for discontinuous galerkin space discretizations applied to wave propagation problems we study the performance of methods of lines combining discontinuous galerkin spatial discretizations and explicit runge kutta time integrators with the aim of deriving optimal runge kutta schemes for wave propagation applications we review relevant runge kutta methods from literature and consider schemes of order q from 3 to 4 and number of stages up to q 4 for optimization from a user point of view the problem of the computational efficiency involves the choice of the best combination of mesh and numerical method two scenarios are defined in the first one the element size is totally free and a 8 stage fourth order runge kutta scheme is found to minimize a cost measure depending on both accuracy and stability in the second one the elements are assumed to be constrained to such a small size by geometrical features of the computational domain that accuracy is disregarded we then derive one 7 stage third order scheme and one 8 stage fourth order scheme that maximize the stability limit the performance of the three new schemes is thoroughly analyzed and the benefits are illustrated with two examples for each of these runge kutta methods we provide the coefficients for a 2n storage implementation along with the information needed by the user to employ them optimally

prefactored small stencil compact schemes abstract a new type of prefactored compact schemes is presented that obtains high order accuracy while using a very small stencil size these schemes require fewer boundary stencils and offer simpler boundary condition implementation than the existing compact schemes results are shown for linear and nonlinear 1 d benchmark problems and a 2 d linear benchmark problem boundary stencils for both exterior and interior multiblock boundaries are given and boundary condition specification is described and demonstrated

runge kutta methods with minimum storage implementations solution of partial differential equations by the method of lines requires the integration of large numbers of ordinary differential equations odes in such computations storage requirements are typically one of the main considerations especially if a high order ode solver is required we investigate runge kutta methods that require only two storage locations per ode existing methods of this type require additional memory if an error estimate or the ability to restart a step is required we present a new more general class of methods that provide error estimates and or the ability to restart a step while still employing the minimum possible number of memory registers examples of such methods are found to have good properties