共查询到20条相似文献,搜索用时 15 毫秒
1.
Identifying the temperature distribution in a parabolice quation with overspecified data using a multiquadric quasi-interpolation method 下载免费PDF全文
In this paper, we use a kind of univariate multiquadric
quasi-interpolation to solve a parabolic equation with overspecified
data, which has arisen in many physical phenomena. We obtain the
numerical scheme by using the derivative of the quasi-interpolation
to approximate the spatial derivative of the dependent variable and
a simple forward difference to approximate the temporal derivative
of the dependent variable. The advantage of the presented scheme is
that the algorithm is very simple so it is very easy to
implement. The results of the numerical experiment are presented and are
compared with the exact solution to confirm the good accuracy of the
presented scheme. 相似文献
2.
In this study, we present a new and very accurate numerical method to approximate the Fisher’s-type equations. Firstly, the
spatial derivative in the proposed equation is approximated by a sixth-order compact finite difference (CFD6) scheme. Secondly,
we solve the obtained system of differential equations using a third-order total variation diminishing Runge–Kutta (TVD-RK3)
scheme. Numerical examples are given to illustrate the efficiency of the proposed method. 相似文献
3.
Pierre-Henri Maire 《Journal of computational physics》2009,228(7):2391-2425
We present a high-order cell-centered Lagrangian scheme for solving the two-dimensional gas dynamics equations on unstructured meshes. A node-based discretization of the numerical fluxes for the physical conservation laws allows to derive a scheme that is compatible with the geometric conservation law (GCL). Fluxes are computed using a nodal solver which can be viewed as a two-dimensional extension of an approximate Riemann solver. The first-order scheme is conservative for momentum and total energy, and satisfies a local entropy inequality in its semi-discrete form. The two-dimensional high-order extension is constructed employing the generalized Riemann problem (GRP) in the acoustic approximation. Many numerical tests are presented in order to assess this new scheme. The results obtained for various representative configurations of one and two-dimensional compressible fluid flows show the robustness and the accuracy of our new scheme. 相似文献
4.
给出抛物方程一种有效的区域分裂差分格式,提高了计算效率.对一阶项采用二阶迎风差分格式,内边界点和各子区域分别采用显隐差分格式.在较弱的稳定性条件下,得到离散l2模误差估计结果.最后给出具体的数值算例,以验证方法的实用性. 相似文献
5.
Jerzy Stanek 《Central European Journal of Physics》2011,9(6):1503-1508
Applying an improved approximation scheme to the centrifugal term, the approximate analytical solutions of the Schrödinger equation for the Eckart potential are presented. Bound state energy eigenvalues and the corresponding eigenfunctions are obtained in closed forms for the arbitrary radial and angular momentum quantum numbers, and different values of the screening parameter. The results are compared with those obtained by the other approximate and numerical methods. It is shown that the present method is systematic, more efficient and accurate. 相似文献
6.
7.
We propose a discretization method of a five-equation model with isobaric closure for the simulation of interfaces between compressible fluids. This numerical solver is a Lagrange–Remap scheme that aims at controlling the numerical diffusion of the interface between both fluids. This method does not involve any interface reconstruction procedure. The solver is equipped with built-in stability and consistency properties and is conservative with respect to mass, momentum, total energy and partial masses. This numerical scheme works with a very broad range of equations of state, including tabulated laws. Properties that ensure a good treatment of the Riemann invariants across the interface are proven. As a consequence, the numerical method does not create spurious pressure oscillations at the interface. We show one-dimensional and two-dimensional classic numerical tests. The results are compared with the approximate solutions obtained with the classic upwind Lagrange–Remap approach, and with experimental and previously published results of a reference test case. 相似文献
8.
9.
We examine a numerical method to approximate to a fractional diffusion equation with the Riesz fractional derivative in a finite domain, which has second order accuracy in time and space level. In order to approximate the Riesz fractional derivative, we use the “fractional centered derivative” approach. We determine the error of the Riesz fractional derivative to the fractional centered difference. We apply the Crank–Nicolson method to a fractional diffusion equation which has the Riesz fractional derivative, and obtain that the method is unconditionally stable and convergent. Numerical results are given to demonstrate the accuracy of the Crank–Nicolson method for the fractional diffusion equation with using fractional centered difference approach. 相似文献
10.
《Physics letters. A》1997,236(3):232-236
It is well known that connected moments expansions when used to approximate the ground-state energy of Hamiltonian systems may suffer from extraneous singularities in various regions of parameter space. In this brief Letter a numerical investigation is presented to study an approximation scheme developed by Ullah to avoid the singularities found in moments expansions. Specifically, we study the single-impurity Wolff model as well as the 32-site Anderson lattice. 相似文献
11.
12.
In this Letter, we present analytical and numerical solutions for an axis-symmetric diffusion-wave equation. For problem formulation, the fractional time derivative is described in the sense of Riemann-Liouville. The analytical solution of the problem is determined by using the method of separation of variables. Eigenfunctions whose linear combination constitute the closed form of the solution are obtained. For numerical computation, the fractional derivative is approximated using the Grünwald-Letnikov scheme. Simulation results are given for different values of order of fractional derivative. We indicate the effectiveness of numerical scheme by comparing the numerical and the analytical results for α=1 which represents the order of derivative. 相似文献
13.
It is the main aim of this paper to investigate the numerical methods of the radiative transfer equation.Using the five-point formula to approximate the differential part and the Simpson formula to substitute for integral part respectively, a new high-precision numerical scheme, which has 4-order local truncation error, is obtained. Subsequently,a numerical example for radiative transfer equation is carried out, and the calculation results show that the new numerical scheme is more accurate. 相似文献
14.
Ali Abbas 《advances in applied mathematics and mechanics.》2014,6(3):327-344
In this paper the problem $-{\rm div}(a(x,y)\nabla u)=f$ with Dirichlet boundary conditions on a square is
solved iteratively with high accuracy for $u$ and $\nabla u$ using a new scheme called
"hermitian box-scheme". The design of the scheme is based on a "hermitian box", combining the
approximation of the gradient by the fourth order hermitian derivative, with a conservative discrete
formulation on boxes of length 2$h$.
The iterative technique is based on the repeated solution by a fast direct method of a discrete Poisson
equation on a uniform rectangular mesh. The problem is suitably scaled before iteration. The numerical
results obtained show the efficiency of the numerical scheme. This work is the extension to strongly
elliptic problems of the hermitian box-scheme presented by Abbas and Croisille (J. Sci. Comput., 49 (2011), pp. 239--267). 相似文献
15.
A Comparative Study of Finite Element and Finite Difference Methods for Two-Dimensional Space-Fractional Advection-Dispersion Equation 下载免费PDF全文
Guofei Pang Wen Chen & Kam Yim Sze 《advances in applied mathematics and mechanics.》2016,8(1):166-186
The paper makes a comparative study of the finite element method (FEM)
and the finite difference method (FDM) for two-dimensional fractional advection-dispersion
equation (FADE) which has recently been considered a promising tool in
modeling non-Fickian solute transport in groundwater. Due to the non-local property
of integro-differential operator of the space-fractional derivative, numerical solution of
FADE is very challenging and little has been reported in literature, especially for high-dimensional
case. In order to effectively apply the FEM and the FDM to the FADE
on a rectangular domain, a backward-distance algorithm is presented to extend the
triangular elements to generic polygon elements in the finite element analysis, and a
variable-step vector Grünwald formula is proposed to improve the solution accuracy of the conventional finite difference scheme. Numerical investigation shows that the
FEM compares favorably with the FDM in terms of accuracy and convergence rate
whereas the latter enjoys less computational effort. 相似文献
16.
In this paper, we introduce a linearized energy-preserving scheme which preserves the discrete global energy of solutions to the improved Korteweg?deVries equation. The method presented is based on the finite volume element method, by resorting to the variational derivative to transform the improved Korteweg?deVries equation into a new form, and then designing energy-preserving schemes for the transformed equation. The proposed scheme is much more efficient than the standard nonlinear scheme and has good stability. To illustrate its efficiency and conservative properties, we also compare it with other nonlinear schemes. Finally, we verify the efficiency and conservative properties through numerical simulations. 相似文献
17.
G. Tomar D. Gerlach G. Biswas N. Alleborn A. Sharma F. Durst S.W.J. Welch A. Delgado 《Journal of computational physics》2007,227(2):1267-1285
A numerical methodology to simulate two-phase electrohydrodynamic flows under the volume-of-fluid paradigm is proposed. The electric force in such systems acts only at the interface and is zero elsewhere in the two fluids. Continuum surface force representations are derived for the electric field force in a system of dielectric–dielectric and conducting–conducting fluids. On the basis of analytical calculations for simple flow problems we propose a weighted harmonic mean interpolation scheme to smoothen the electric properties in the diffused transition region (interface). It is shown that a wrong choice of interpolation scheme (weighted arithmetic mean) may lead to a transition region thickness dependent electric field in the bulk. We simulate a set of problems with exact or approximate analytical solutions to validate the numerical model proposed. A coupled level set and volume-of-fluid (CLSVOF) algorithm has been used for simulations presented here. 相似文献
18.
We present a numerical scheme for the approximation of nonlinear evolution equations over large time intervals. Our algorithm is motivated from the dynamical systems point of view. In particular, we adapt the methodology of approximate inertial manifolds to a finite difference scheme. This leads to a differential treatment in which the higher (i.e. unresolved) modes are expressed in terms of the lower modes. As a particular example we derive an approximate inertial manifold for Burgers' equation and develop a numerical algorithm suitable for computing. We perform a parameter study in which we compare the accuracy of a standard scheme with our modified scheme. For all values of the parameters (which are the coefficient of viscosity and the cell size), we obtain a decrease in the numerical error by at least a factor of 2.0 with the modified scheme. The decrease in error is substantially greater over large regions of the parameters space. 相似文献
19.
《Journal of computational physics》2008,227(2):1267-1285
A numerical methodology to simulate two-phase electrohydrodynamic flows under the volume-of-fluid paradigm is proposed. The electric force in such systems acts only at the interface and is zero elsewhere in the two fluids. Continuum surface force representations are derived for the electric field force in a system of dielectric–dielectric and conducting–conducting fluids. On the basis of analytical calculations for simple flow problems we propose a weighted harmonic mean interpolation scheme to smoothen the electric properties in the diffused transition region (interface). It is shown that a wrong choice of interpolation scheme (weighted arithmetic mean) may lead to a transition region thickness dependent electric field in the bulk. We simulate a set of problems with exact or approximate analytical solutions to validate the numerical model proposed. A coupled level set and volume-of-fluid (CLSVOF) algorithm has been used for simulations presented here. 相似文献
20.
三维高超声速无粘定常绕流的数值模拟 总被引:13,自引:0,他引:13
本文采用一种简单有效的通量分裂结合一种二阶TVD格式的数值通量的方法,提出一种隐式的迎风有限体积格式,并利用这种格式,从气体动力学非定常Euler方程组出发,数值模拟了三维不对称物体的高超声速无粘定常绕流。数值结果表明此格式具有分辨率较高和收敛速度较快的优点。 相似文献