### Abstract

A new numerical scheme is proposed for the dispersion-convection equation which combines the utility of a fixed grid in Eulerian coordinates with the computational power of the Lagrangian method. Convection is formally decoupled from dispersion in a manner which does not leave room for ambiguity. The resulting convection problem is solved by the method of characteristics on a grid fixed in space. Dispersion is handled by finite elements on a separate grid which may, but need not, coincide wit the former at selected points in spacetime. Information is projected from one grid to another by local interpolation. The conjugate grid method is implemented by linear finite elements in conjunction with piecewise linear interpolation functions and applied to five problems ranging from predominant dispersion to pure convection. The results are entirely free of oscillations. Numerical dispersion exists but can be brought under control either by reducing the spatial increment, or by increasing the time step size, of the grid used to solve the convection problem. Contrary to many other methods, best results are often obtained when the Courant number exceeds 1.

Original language | English (US) |
---|---|

Pages (from-to) | 270-294 |

Number of pages | 25 |

Journal | Journal of Computational Physics |

Volume | 41 |

Issue number | 2 |

DOIs | |

State | Published - 1981 |

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### ASJC Scopus subject areas

- Computer Science Applications
- Physics and Astronomy(all)

### Cite this

**A Eulerian-Lagrangian numerical scheme for the dispersion-convection equation using conjugate space-time grids.** / Neuman, Shlomo P.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - A Eulerian-Lagrangian numerical scheme for the dispersion-convection equation using conjugate space-time grids

AU - Neuman, Shlomo P

PY - 1981

Y1 - 1981

N2 - A new numerical scheme is proposed for the dispersion-convection equation which combines the utility of a fixed grid in Eulerian coordinates with the computational power of the Lagrangian method. Convection is formally decoupled from dispersion in a manner which does not leave room for ambiguity. The resulting convection problem is solved by the method of characteristics on a grid fixed in space. Dispersion is handled by finite elements on a separate grid which may, but need not, coincide wit the former at selected points in spacetime. Information is projected from one grid to another by local interpolation. The conjugate grid method is implemented by linear finite elements in conjunction with piecewise linear interpolation functions and applied to five problems ranging from predominant dispersion to pure convection. The results are entirely free of oscillations. Numerical dispersion exists but can be brought under control either by reducing the spatial increment, or by increasing the time step size, of the grid used to solve the convection problem. Contrary to many other methods, best results are often obtained when the Courant number exceeds 1.

AB - A new numerical scheme is proposed for the dispersion-convection equation which combines the utility of a fixed grid in Eulerian coordinates with the computational power of the Lagrangian method. Convection is formally decoupled from dispersion in a manner which does not leave room for ambiguity. The resulting convection problem is solved by the method of characteristics on a grid fixed in space. Dispersion is handled by finite elements on a separate grid which may, but need not, coincide wit the former at selected points in spacetime. Information is projected from one grid to another by local interpolation. The conjugate grid method is implemented by linear finite elements in conjunction with piecewise linear interpolation functions and applied to five problems ranging from predominant dispersion to pure convection. The results are entirely free of oscillations. Numerical dispersion exists but can be brought under control either by reducing the spatial increment, or by increasing the time step size, of the grid used to solve the convection problem. Contrary to many other methods, best results are often obtained when the Courant number exceeds 1.

UR - http://www.scopus.com/inward/record.url?scp=0001998744&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0001998744&partnerID=8YFLogxK

U2 - 10.1016/0021-9991(81)90097-8

DO - 10.1016/0021-9991(81)90097-8

M3 - Article

AN - SCOPUS:0001998744

VL - 41

SP - 270

EP - 294

JO - Journal of Computational Physics

JF - Journal of Computational Physics

SN - 0021-9991

IS - 2

ER -