### Abstract

We propose an integrable discrete model of one-dimensional soil water infiltration. This model is based on the continuum model by Broadbridge and White, which takes the form of nonlinear convection–diffusion equation with a nonlinear flux boundary condition at the surface. It is transformed to the Burgers equation with a time-dependent flux term by the hodograph transformation. We construct a discrete model preserving the underlying integrability, which is formulated as the self-adaptive moving mesh scheme. The discretization is based on linearizability of the Burgers equation to the linear diffusion equation, but the naïve discretization based on the Euler scheme which is often used in the theory of discrete integrable systems does not necessarily give a good numerical scheme. Taking desirable properties of a numerical scheme into account, we propose an alternative discrete model that produces solutions with similar accuracy to direct computation on the original nonlinear equation, but with clear benefits regarding computational cost.

Original language | English |
---|---|

Pages (from-to) | 483-507 |

Number of pages | 25 |

Journal | Studies in Applied Mathematics |

Volume | 140 |

Issue number | 4 |

DOIs | |

Publication status | Published - May 2018 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Applied Mathematics

### Cite this

*Studies in Applied Mathematics*,

*140*(4), 483-507. https://doi.org/10.1111/sapm.12208

**Integrable Discrete Model for One-Dimensional Soil Water Infiltration.** / Triadis, Dimetre; Broadbridge, Philip; Kajiwara, Kenji; Maruno, Ken Ichi.

Research output: Contribution to journal › Article

*Studies in Applied Mathematics*, vol. 140, no. 4, pp. 483-507. https://doi.org/10.1111/sapm.12208

}

TY - JOUR

T1 - Integrable Discrete Model for One-Dimensional Soil Water Infiltration

AU - Triadis, Dimetre

AU - Broadbridge, Philip

AU - Kajiwara, Kenji

AU - Maruno, Ken Ichi

PY - 2018/5

Y1 - 2018/5

N2 - We propose an integrable discrete model of one-dimensional soil water infiltration. This model is based on the continuum model by Broadbridge and White, which takes the form of nonlinear convection–diffusion equation with a nonlinear flux boundary condition at the surface. It is transformed to the Burgers equation with a time-dependent flux term by the hodograph transformation. We construct a discrete model preserving the underlying integrability, which is formulated as the self-adaptive moving mesh scheme. The discretization is based on linearizability of the Burgers equation to the linear diffusion equation, but the naïve discretization based on the Euler scheme which is often used in the theory of discrete integrable systems does not necessarily give a good numerical scheme. Taking desirable properties of a numerical scheme into account, we propose an alternative discrete model that produces solutions with similar accuracy to direct computation on the original nonlinear equation, but with clear benefits regarding computational cost.

AB - We propose an integrable discrete model of one-dimensional soil water infiltration. This model is based on the continuum model by Broadbridge and White, which takes the form of nonlinear convection–diffusion equation with a nonlinear flux boundary condition at the surface. It is transformed to the Burgers equation with a time-dependent flux term by the hodograph transformation. We construct a discrete model preserving the underlying integrability, which is formulated as the self-adaptive moving mesh scheme. The discretization is based on linearizability of the Burgers equation to the linear diffusion equation, but the naïve discretization based on the Euler scheme which is often used in the theory of discrete integrable systems does not necessarily give a good numerical scheme. Taking desirable properties of a numerical scheme into account, we propose an alternative discrete model that produces solutions with similar accuracy to direct computation on the original nonlinear equation, but with clear benefits regarding computational cost.

UR - http://www.scopus.com/inward/record.url?scp=85042529353&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85042529353&partnerID=8YFLogxK

U2 - 10.1111/sapm.12208

DO - 10.1111/sapm.12208

M3 - Article

AN - SCOPUS:85042529353

VL - 140

SP - 483

EP - 507

JO - Studies in Applied Mathematics

JF - Studies in Applied Mathematics

SN - 0022-2526

IS - 4

ER -