Articles you may be interested inDevelopment of an equation of state for electrolyte solutions by combining the statistical associating fluid theory and the mean spherical approximation for the nonprimitive modelThe variational mean spherical scaling approximation ͑VMSSA͒ is extended to nonspherical objects in ionic solutions. The mean spherical approximation ͑MSA͒ and the binding mean spherical approximation ͑BIMSA͒ are extensions of the linearized Poisson-Boltzmann ͑or Debye-Hückel͒ approximation that treat the excluded volume of all the ions in the system in a symmetric and consistent way. For systems with Coulomb and screened Coulomb interactions in a variety of mean spherical derived approximations, it has been recently shown that the solution of the Ornstein-Zernike ͑OZ͒ equation is given in terms of a screening parameter matrix ⌫ = . This includes the ''primitive'' model of electrolytes, in which the solvent is a continuum dielectric, but also models in which the solvent is a dipolar hard sphere, and much more recently the YUKAGUA model of water that reproduces the known neutron diffraction experiments of water quite well. The MSA can be deduced from a variational principle in which the energy is obtained from simple electrostatic considerations and the entropy is a universal function. For the primitive model it is ⌬S ϭϪk(⌫ 3 /3). For other models this function is more complex, but can always be expressed as an integral of known functions. We propose now a natural extension of this principle to nonspherical objects, such as dumbbells, in which the equivalence to the OZ approach can be explicitly verified.
We present a numerical study of an adaptive technique for solving steady fluid flow problems through porous media in 2D using a discontinuous Galerkin (DG) method, the so‐called Local Discontinuous Galerkin (LDG) method. DG methods may be viewed as high‐order extensions of the classical finite volume method and, since no interelement continuity is imposed, they can be defined on very general meshes, including nonconforming meshes, making these methods suitable for h‐adaptivity. The technique starts with an initial conformal spatial discretization of the domain and, in each step, the error of the solution is estimated. The mesh is locally modified according to the error estimate by performing two local operations: refinement and agglomeration. This procedure is repeated until the solution reaches a desired accuracy. The performance of this technique is examined through several numerical experiments and results are compared with globally refined meshes in examples with known analytic solutions.
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