Spatial Finite Difference Approximations for Wave-Type Equations

نویسندگان

  • Bengt Fornberg
  • Michelle Ghrist
چکیده

The simplest finite difference approximations for spatial derivatives are centered, explicit, and applied to “regular” equispaced grids. Well-established generalizations include the use of implicit (compact) approximations and staggered grids. We find here that the combination of these two concepts, together with high formal order of accuracy, is very effective for approximating the first derivatives in space that occur in many wave-type PDEs.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Upwind schemes for the wave equation in second-order form

We develop new high-order accurate upwind schemes for the wave equation in second-order form. These schemes are developed directly for the equations in second-order form, as opposed to transforming the equations to a first-order hyperbolic system. The schemes are based on the solution to a local Riemann-type problem that uses d’Alembert’s exact solution. We construct conservative finite differe...

متن کامل

On Consistency of Finite Difference Approximations to the Navier-Stokes Equations

In the given paper, we confront three finite difference approximations to the Navier–Stokes equations for the two-dimensional viscous incomressible fluid flows. Two of these approximations were generated by the computer algebra assisted method proposed based on the finite volume method, numerical integration, and difference elimination. The third approximation was derived by the standard replac...

متن کامل

Nonsmooth data error estimates for approximations of an evolution equation with a positive-type memory term

We study the numerical approximation of an integro-differential equation which is intermediate between the heat and wave equations. The proposed discretization uses convolution quadrature based on the firstand second-order backward difference methods in time, and piecewise linear finite elements in space. Optimal-order error bounds in terms of the initial data and the inhomogeneity are shown fo...

متن کامل

Tl . - - - - - AIAA - 99 - 0966 Detonation Solutions from Reactive Navier - Stokes Equations

Two-dimensional reactive Navier-Stokes equations are solved using a simple implicit Beam-Warming finite difference scheme. Comparisons of the detonation wave solutions of reactive Euler equations and reactive Navier-Stokes equations show that physical diffusion is important at high resolution when the numerical diffusion becomes negligible. Hence, for accurate detonation wave solutions it is ne...

متن کامل

Solution of propagation of acoustic-gravity waves in the atmosphere using finite difference method of order two

Investigating waves propagation’s equation in the atmosphere is one of the important and widely used issues in various sciences, which has attracted many researchers. A type of propagating waves is an acoustic-gravity wave. These type of waves have a lot of stationarity properties and can be propagate to a high altitude in the atmosphere. The equation of acoustic-gravity wave propagation is a h...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • SIAM J. Numerical Analysis

دوره 37  شماره 

صفحات  -

تاریخ انتشار 1999