We construct the Navier-Stokes equation from first principle using relativistic bosonic lagrangian which is invariant under local gauge transformations. We show that by defining the bosonic field to represent the dynamic of fluid in a particular form, a general Navier-Stokes equation with conservative forces can be reproduced exactly. It also induces two new forces, one is relevant for rotation...

Numerical algorithms for solving problems of mathematical physics on modern parallel computers employ various domain decomposition techniques. Domain decomposition schemes are developed here to solve numerically initial/boundary value problems for the Stokes system of equations in the primitive variables pressure-velocity. Unconditionally stable schemes of domain decomposition are based on the ...

Current FEM software projects have made significant advances in various automated modeling techniques. We present some of the mathematical abstractions employed by these projects that allow a user to switch between finite elements, linear solvers, mesh refinement and geometry, and weak forms with very few modifications to the code. To evaluate the modularity provided by one of these abstraction...

We establish a representation of the solution of 3d Navier-Stokes equations in the space Φ(α, α) using sums over rooted trees. We study the convergence properties of this series recovering in a simplified manner some results obtained recently by Sinai and other known results. The series representation make sense also in the critical case where there exists global solutions for small initial data.

We present formulations of the Trotter-Kato theorem for approximation of linear C0-semigroups which provide very useful framework when convergence of numerical approximations to solutions of PDEs are studied. Applicability of our results is demonstrated using a first order hyperbolic equation, a wave equation and Stokes’ equation as illustrative examples.

We construct wavelet Riesz bases for the usual Sobolev spaces of divergence free functions on (0, 1)n that have vanishing normals at the boundary. We give a simultaneous space-time variational formulation of the instationary Stokes equations that defines a boundedly invertible mapping between a Bochner space and the dual of another Bochner space. By equipping these Bochner spaces by tensor prod...

The additive turbulent decomposition (ATD) method is a computational scheme for solving the Navier–Stokes equations and related nonlinear dissipative evolution equations. It involves a decomposition of the Navier–Stokes equation into equations for largeand small-scale components similar in spirit, but different in details, to the nonlinear Galerkin methods proposed by Temam and coworkers. In th...

The Navier-Stokes equations describe a large class of fluid flows but are difficult to solve analytically because of their nonlinearity. We present in this paper a parallel solver for the 3-D Navier-Stokes equations of incompressible unsteady flows with constant coefficients, discretized by the finite difference method. We apply the prediction-projection method which transforms the Navier-Stoke...