burgers_exact

burgers_exact, a MATLAB code which evaluates exact solutions of the time-dependent 1D viscous Burgers equation.

The form of the Burgers equation considered here is:

        du       du        d^2 u
        -- + u * -- = nu * -----
        dt       dx        dx^2
      

Licensing:

The information on this web page is distributed under the MIT license.

Languages:

burgers_exact is available in a C version and a C++ version and a Fortran77 version and a Fortran90 version and a MATLAB version and an Octave version and a Python version.

Related Data and Programs:

burgers_exact_test

burgers, a dataset directory which contains 40 solutions of the Burgers equation in one space dimension and time, at equally spaced times from 0 to 1, with values at 41 equally spaced nodes in [0,1];

burgers_steady_viscous, a MATLAB code which solves the steady (time-independent) viscous Burgers equation using a finite difference discretization of the conservative form of the equation, and then applying Newton's method to solve the resulting nonlinear system.

fd1d_burgers_lax, a MATLAB code which applies the finite difference method and the Lax-Wendroff method to solve the non-viscous Burgers equation in one spatial dimension and time.

fd1d_burgers_leap, a MATLAB code which applies the finite difference method and the leapfrog approach to solve the non-viscous Burgers equation in one spatial dimension and time.

kdv_exact, a MATLAB code which evaluates an exact solution of the Korteweg-deVries (KdV) partial differential equation (PDE).

navier_stokes_2d_exact, a MATLAB code which evaluates an exact solution to the incompressible time-dependent Navier-Stokes equations (NSE) over an arbitrary domain in 2D.

navier_stokes_3d_exact, a MATLAB code which evaluates an exact solution to the incompressible time-dependent Navier-Stokes equations (NSE) over an arbitrary domain in 3D.

pendulum_nonlinear_exact, a MATLAB code which evaluates an exact formula for the solution of the the ordinary differential equations (ODE) that represent the behavior of a nonlinear pendulum of length L under a gravitational force of strength G.

spiral_exact, a MATLAB code which computes a 2D velocity vector field that is an exact solution of the continuity equation.

stokes_2d_exact, a MATLAB code which evaluates exact solutions to the incompressible steady Stokes equations over the unit square in 2D.

Reference:

1. Claude Basdevant, Michel Deville, Pierre Haldenwang, J Lacroix, J Ouazzani, Roger Peyret, Paolo Orlandi, Anthony Patera,
   Spectral and finite difference solutions of the Burgers equation,
   Computers and Fluids,
   Volume 14, Number 1, 1986, pages 23-41.

Source Code:

• burgers_viscous_time_exact1.m, evaluates exact solution #1 to the Burgers equation.
• burgers_viscous_time_exact2.m, evaluates exact solution #2 to the Burgers equation.
• hermite_ek_compute.m, computes a Gauss-Hermite quadrature rule.
• imtqlx.m, diagonalizes a symmetric tridiagonal matrix.
• r8_sign.m, returns the sign of an R8.
• r8mat_print.m, prints an R8MAT.
• r8mat_print_some.m, prints some of an R8MAT.
• r8mat_write.m, writes an R8MAT file.
• r8vec_print.m, prints an R8VEC.