Starting with the solution of Maxwell's equations based on the volume integral equation (VIE) method, the transition to a volume-surface integral equation (VSIE) formulation is described. For the VSIE method, a generalized calculation method is developed to help us directly determine E fields at...
We need to know what the trade-off is, but first we need a high-order Navier-Stokes' equations solver for unstructured meshes.Michael Van AltenaCarl F. Ollivier-GoochCFD 99M. Van Altena and C. Ollivier-Gooch. Finite-volume methods for solving laplace equation on unstructured triangular meshes...
Two novel numerical methods with a nonlocal operator (using nodal basis functions) for the space-fractional Boussinesq equation are derived. These methods are based on the finite volume and finite element methods, respectively. Finally, some numerical results using fractional Boussinesq equation with ...
afully elliptic Navier–Stokes procedure.[translate] aproposed. Hwang and Lai [10] investigated numerically laminar[translate] aflow in a circular tube at constant heat flux boundary condition.[translate] afor solving the energy equation and a control volume method[translate]...
The unstructured grid solver is based on a mixed finite volume/finite element approach. Equivalence conditions linking the node-centered finite volume and the linear Lagrangian finite element scheme over unstructured grids are reported and used to devise a common framework for solving the discrete ...
Differentiating equation (5-46) with respect to the volume at the critical point results in (5-49)[∂p∂V]Tc,pc=−RTc(Vc−b)2+2aVc3=0 (5-50)[∂2p∂V2]Tc,pc=2RTc(Vc−b)3+6aVc4=0 Solving equations (5-49) and (5-50) simultaneously for the parameters a and b gi...
It is the purpose of this paper to present a numerical algorithm for solving this equation, and to apply it to the problem of shock structure in a one-dimensional flow. It will be seen that the method of solution generalizes to problems involving other molecular models and more space ...
Scientific Reports volume 13, Article number: 1549 (2023) Cite this article 1147 Accesses Metrics details Abstract In this article, we developed a new higher-order implicit finite difference iterative scheme (FDIS) for the solution of the two dimension (2-D) time fractional Cable equation (FCE)...
Rearranging, and solving for ψ, (5.3j)ψ=9.96×10-2 J C-1. One can solve for ψ at the other distances, using the approach above. The ψ values for the other x values are ψ = 4.58 × 10−2 J C−1 for x = 5 × 10−9 m, ψ = 2.72 × 10−2 J C−1 for...
which is a useful relation for understanding the boundary values of Moran’s index. Especially, Eq. (24) reflects the relationship between the model’s constant term, a, and Moran’s index, I. Least squares algorithm The premise of application of a mathematical model to solving real problems...