共查询到20条相似文献,搜索用时 15 毫秒
1.
Imanol Garcia-Beristain Lakhdar Remaki 《Numerical Methods for Partial Differential Equations》2023,39(1):329-355
Time efficiency is one of the more critical concerns in computational fluid dynamics simulations of industrial applications. Extensive research has been conducted to improve the underlying numerical schemes to achieve time process reduction. Within this context, this paper presents a new time discretization method based on the Adomian decomposition technique for Euler equations. The obtained scheme is time-order adaptive; the order is automatically adjusted at each time step and over the space domain, leading to significant processing time reduction. The scheme is formulated in an appropriate recursive formula, and its efficiency is demonstrated through numerical tests by comparison to exact solutions and the popular Runge–Kutta-discontinuous Galerkin method. 相似文献
2.
Athanassios G. Bratsos 《Numerical Algorithms》2007,46(1):45-58
A predictor–corrector (P-C) scheme is applied successfully to a nonlinear method arising from the use of rational approximants
to the matrix-exponential term in a three-time level recurrence relation. The resulting nonlinear finite-difference scheme,
which is analyzed for local truncation error and stability, is solved using a P-C scheme, in which the predictor and the corrector
are explicit schemes of order 2. This scheme is accelerated by using a modification (MPC) in which the already evaluated values
are used for the corrector. The behaviour of the P-C/MPC schemes is tested numerically on the Boussinesq equation already
known from the bibliography free of boundary conditions. The numerical results are derived for both the bad and the good Boussinesq
equation and conclusions from the relevant known results are derived.
相似文献
3.
Frédéric Nataf 《Comptes Rendus Mathematique》2005,340(10):775-778
Based on a PML for the advective wave equation, we propose two PML models for the linearized Euler equations. The derivation of the first model can be applied to other physical models. The second model was implemented. Numerical results are shown. To cite this article: F. Nataf, C. R. Acad. Sci. Paris, Ser. I 340 (2005). 相似文献
4.
《Applied Numerical Mathematics》1986,2(6):475-493
An iterative method is developed for the solution of the steady Euler equations for inviscid flow. The system of hyperbolic conservation laws is discretized by a finite-volume Osher-discretization. The iterative method is a multiple grid (FAS) iteration with symmetric Gauss-Seidel (SGS) as a relaxation method. Initial estimates are obtained by full multigrid (FMG). In the pointwise relaxation the equations are kept in block-coupled form and local linearization of the equations and the boundary conditions is considered. The efficient formulation of Osher's discretization of the 2-D non-isentropic steady Euler equations and its linearization is presented. The efficiency of FAS-SGS iteration is shown for a transonic model problem. It appears that, for the problem considered, the rate of convergence is almost independent of the gridsize and that for all meshsizes the discrete system is solved up to truncation error accuracy in only a few (2 or 3) iteration cycles. 相似文献
5.
Rentaro Agemi 《偏微分方程通讯》2013,38(6):645-681
6.
L. C. Cabrera L. B. Barichello 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2006,57(2):285-312
An analytical version of the discrete-ordinates method is used to derive solutions for a class of problems defined in terms
of the S-model kinetic equations. In addition to a general derivation, which is common to all the problems, specific analytical
and computational aspects for each one of the problems are presented. In particular, numerical results for velocity profile,
heat-flow profile and flow rates are obtained with high accuracy for the plane channel problems. In the case of half-space
problems, the thermal and viscous-slip coefficients are also listed.
Received: September 20, 2004; revised: March 31, 2005 相似文献
7.
M. V. Abakumov A. M. Galanina V. A. Isakov N. N. Tyurina A. P. Favorskii A. B. Khrulenko 《Differential Equations》2011,47(8):1103-1109
We suggest an original scheme and an algorithm for the numerical solution of the Euler equations of gas dynamics. The construction
of the scheme is based on the mass, momentum, and energy conservation laws. The flux computation is carried out by summation
of elementary fluxes formed by small-amplitude running waves that satisfy the linearized equations of gas dynamics. The scheme
contains no artificial regularizers, has second-order accuracy on smooth solutions, and is quasimonotone in a neighborhood
of the discontinuities. Examples of one- and two-dimensional computations are given. 相似文献
8.
The parabolic equation with the control parameter is a class of parabolic inverse problems and is nonlinear. While determining the solution of the problems, we shall determinate some unknown control parameter. These problems play a very important role in many branches of science and engineering. The article is devoted to the following parabolic initial-boundary value problem with the control parameter: ∂u/∂t=∂2u/∂x2+p(t)u+?(x,t),0<x<1,0<t?T satisfying u(x,0)=f(x),0<x<1; u(0,t)=g0(t), u(1,t)=g1(t), u(x∗,t)=E(t),0?t?T where ?(x,t),f(x),g0(t),g1(t) and E(t) are known functions, u(x,t) and p(t) are unknown functions. A linearized compact difference scheme is constructed. The discretization accuracy of the difference scheme is two order in time and four order in space. The solvability of the difference scheme is proved. Some numerical results and comparisons with the difference scheme given by Dehghan are presented. The numerical results show that the linearized difference scheme of this article improve the accuracy of the space and time direction and shorten computation time largely. The method in this article is also applicable to the two-dimensional inverse problem. 相似文献
9.
Convergence of block iterative methods for linear systems arising in the numerical solution of Euler equations 总被引:3,自引:0,他引:3
Summary We discuss block matrices of the formA=[A
ij
], whereA
ij
is ak×k symmetric matrix,A
ij
is positive definite andA
ij
is negative semidefinite. These matrices are natural block-generalizations of Z-matrices and M-matrices. Matrices of this type arise in the numerical solution of Euler equations in fluid flow computations. We discuss properties of these matrices, in particular we prove convergence of block iterative methods for linear systems with such system matrices. 相似文献
10.
Reinhard Nabben 《Numerische Mathematik》1992,63(1):411-431
Summary We study block matricesA=[Aij], where every blockA
ij
k,k
is Hermitian andA
ii
is positive definite. We call such a matrix a generalized H-matrix if its block comparison matrix is a generalized M-matrix. These matrices arise in the numerical solution of Euler equations in fluid flow computations and in the study of invariant tori of dynamical systems. We discuss properties of these matrices and we give some equivalent conditions for a matrix to be a generalized H-matrix.Research supported by the Graduiertenkolleg mathematik der Universität Bielefeld 相似文献
11.
The fast Fourier transform and the numerical solution of one-dimensional boundary integral equations
Summary Here we present a fully discretized projection method with Fourier series which is based on a modification of the fast Fourier transform. The method is applied to systems of integro-differential equations with the Cauchy kernel, boundary integral equations from the boundary element method and, more generally, to certain elliptic pseudodifferential equations on closed smooth curves. We use Gaussian quadratures on families of equidistant partitions combined with the fast Fourier transform. This yields an extremely accurate and fast numerical scheme. We present complete asymptotic error estimates including the quadrature errors. These are quasioptimal and of exponential order for analytic data. Numerical experiments for a scattering problem, the clamped plate and plane estatostatics confirm the theoretical convergence rates and show high accuracy. 相似文献
12.
13.
Summary We study the approximation problem ofE
f(X
T
) byE
f(X
T
n
), where (X
t
) is the solution of a stochastic differential equation, (X
T
n
) is defined by the Euler discretization scheme with stepT/n, andf is a given function. For smoothf's, Talay and Tubaro have shown that the errorE
f(X
T
) –f(X
T
n
) can be expanded in powers of 1/n, which permits to construct Romberg extrapolation precedures to accelerate the convergence rate. Here, we prove that the expansion exists also whenf is only supposed measurable and bounded, under an additional nondegeneracy condition of Hörmander type for the infinitesimal generator of (X
t
): to obtain this result, we use the stochastic variations calculus. In the second part of this work, we will consider the density of the law ofX
T
n
and compare it to the density of the law ofX
T
. 相似文献
14.
Complex variable boundary integral equations are derived using of holomorphicity theorems for plane harmonic problems concerning unit structures with inclusions, pores and lines of discontinuity of the potential and/or the flow. Unlike the method of analytical elements, the equations cover problems in which discontinuities in the potential, flow and conductance can simultaneously be encountered at the contact points. Versions of the equations are given for connected half planes and for periodic and biperiodic problems. Formulae are obtained which determine the effective impedance tensor of the equivalent homogeneous medium in cases when the unit structure is biperiodic or when the representative volume of a structured medium is identified with the basic cell of a biperiodic system. Recurrence quadrature formulae are proposed which enable one to solve the resulting equations effectively using the complex variable boundary element method. They indicate the computational advantages of using the complex variable method compared with the real variable method: the three integrals appearing in the resulting equations are evaluated analytically in the case of linear elements (regular and singular) with the densities approximated using algebraic polynomials of arbitrary degree. In the case of elements (regular and singular) in the form of an arc of a circle, only one integral requires numerical integration when the densities are approximated using complex trigonometrical polynomials of arbitrary degree. It is emphasized that the combination of the linear and curved boundary elements which have been developed enables the smooth part of a contour to be approximated while retaining the continuity of the tangent and avoiding the complications which arise when the smoothness of the approximation of a contour is ensured using conformal mapping. Examples are presented which illustrate the computational merits of the method developed. They show a sharp increase in accuracy (by orders of magnitude) when curved elements are used for the curvilinear parts of a contour and when terminal elements are used to calculate the flow intensity coefficient at singular points (the crack tips the vertices of angular notches and the common vertices of the units of the medium). 相似文献
15.
《Nonlinear Analysis: Theory, Methods & Applications》2005,60(6):993-1001
In this paper, we prove an existence theorem of global smooth solutions to the Cauchy problem for the one-dimensional relativistic Euler equations. The analysis is based on a priori estimates which are obtained by the characteristic method and maximum principle. 相似文献
16.
P. N. Vabishchevich A. O. Vasil’ev 《Computational Mathematics and Mathematical Physics》2017,57(5):843-853
An algorithm is proposed for selecting a time step for the numerical solution of boundary value problems for parabolic equations. The solution is found by applying unconditionally stable implicit schemes, while the time step is selected using the solution produced by an explicit scheme. Explicit computational formulas are based on truncation error estimation at a new time level. Numerical results for a model parabolic boundary value problem are presented, which demonstrate the performance of the time step selection algorithm. 相似文献
17.
Christophe Berthon Michael Breuß Marc‐Olivier Titeux 《Numerical Methods for Partial Differential Equations》2006,22(2):484-505
In the present work, we consider the numerical approximation of pressureless gas dynamics in one and two spatial dimensions. Two particular phenomena are of special interest for us, namely δ‐shocks and vacuum states. A relaxation scheme is developed which reliably captures these phenomena. In one space dimension, we prove the validity of several stability criteria, i.e., we show that a maximum principle as well as the TVD property for the discrete velocity component and the validity of discrete entropy inequalities hold. Several numerical tests considering not only the developed first‐order scheme but also a classical MUSCL‐type second‐order extension confirm the reliability and robustness of the relaxation approach. The article extends previous results on the topic: the stability conditions for relaxation methods for the pressureless case are refined, useful properties for the time stepping procedure are established, and two‐dimensional numerical results are presented. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006 相似文献
18.
In this paper, we propose a new method to compute the numerical flux of a finite volume scheme, used for the approximation
of the solution of the nonlinear partial differential equation ut+div(qf(u))−ΔΦ(u)=0 in a 1D, 2D or 3D domain. The function Φ is supposed to be strictly increasing, but some values s such that Φ′(s)=0 can exist. The method is based on the solution, at each interface between two control volumes, of the nonlinear elliptic
two point boundary value problem (qf(υ)+(Φ(υ))′)′=0 with Dirichlet boundary conditions given by the values of the discrete approximation in both control volumes. We prove
the existence of a solution to this two point boundary value problem. We show that the expression for the numerical flux can
be yielded without referring to this solution. Furthermore, we prove that the so designed finite volume scheme has the expected
stability properties and that its solution converges to the weak solution of the continuous problem. Numerical results show
the increase of accuracy due to the use of this scheme, compared to some other schemes. 相似文献
19.
A simple, effective technique is described and tested for reducing the variation in estimated expectations of functions of functions of solutions of stochastic differential equations. The technique is implemented with extrapolated Euler method for numerical solution of stochastic differential equations 相似文献
20.
Numerical Algorithms - In this paper, we study a fast linearized numerical method for solving nonlinear time-fractional diffusion equations. A new weighted method is proposed to construct... 相似文献