@article{fdi:010068323,
  title = {{T}he {H}enry problem : new semianalytical solution for velocity-dependent dispersion},
  author = {{F}ahs, {M}. and {A}taie-{A}shtiani, {B}. and {Y}ounes, {A}nis and {S}immons, {C}. {T}. and {A}ckerer, {P}.},
  editor = {},
  language = {{ENG}},
  abstract = {{A} new semianalytical solution is developed for the velocity-dependent dispersion {H}enry problem using the {F}ourier-{G}alerkin method ({FG}). {T}he integral arising from the velocity-dependent dispersion term is evaluated numerically using an accurate technique based on an adaptive scheme. {N}umerical integration and nonlinear dependence of the dispersion on the velocity render the semianalytical solution impractical. {T}o alleviate this issue and to obtain the solution at affordable computational cost, a robust implementation for solving the nonlinear system arising from the {FG} method is developed. {I}t allows for reducing the number of attempts of the iterative procedure and the computational cost by iteration. {T}he accuracy of the semianalytical solution is assessed in terms of the truncation orders of the {F}ourier series. {A}n appropriate algorithm based on the sensitivity of the solution to the number of {F}ourier modes is used to obtain the required truncation levels. {T}he resulting {F}ourier series are used to analytically evaluate the position of the principal isochlors and metrics characterizing the saltwater wedge. {T}hey are also used to calculate longitudinal and transverse dispersive fluxes and to provide physical insight into the dispersion mechanisms within the mixing zone. {T}he developed semianalytical solutions are compared against numerical solutions obtained using an in house code based on variant techniques for both space and time discretization. {T}he comparison provides better confidence on the accuracy of both numerical and semianalytical results. {I}t shows that the new solutions are highly sensitive to the approximation techniques used in the numerical code which highlights their benefits for code benchmarking.},
  keywords = {density-driven flow ; velocity-dependent dispersion ; {H}enry problem ; semianalytical solution ; code benchmarking},
  booktitle = {},
  journal = {{W}ater {R}esources {R}esearch},
  volume = {52},
  numero = {9},
  pages = {7382--7407},
  ISSN = {0043-1397},
  year = {2016},
  DOI = {10.1002/2016wr019288},
  URL = {https://www.documentation.ird.fr/hor/fdi:010068323},
}