Search results for "eulerian method"
showing 4 items of 4 documents
MAST solution of advection problems in irrotational flow fields
2007
Abstract A new numerical–analytical Eulerian procedure is proposed for the solution of convection-dominated problems in the case of existing scalar potential of the flow field. The methodology is based on the conservation inside each computational elements of the 0th and 1st order effective spatial moments of the advected variable. This leads to a set of small ODE systems solved sequentially, one element after the other over all the computational domain, according to a MArching in Space and Time technique. The proposed procedure shows the following advantages: (1) it guarantees the local and global mass balance; (2) it is unconditionally stable with respect to the Courant number, (3) the so…
MAST-RT0 solution of the incompressible Navier–Stokes equations in 3D complex domains
2020
A new numerical methodology to solve the 3D Navier-Stokes equations for incompressible fluids within complex boundaries and unstructured body-fitted tetrahedral mesh is presented and validated with three literature and one real-case tests. We apply a fractional time step procedure where a predictor and a corrector problem are sequentially solved. The predictor step is solved applying the MAST (Marching in Space and Time) procedure, which explicitly handles the non-linear terms in the momentum equations, allowing numerical stability for Courant number greater than one. Correction steps are solved by a Mixed Hybrid Finite Elements discretization that assumes positive distances among tetrahedr…
A marching in space and time (MAST) solver of the shallow water equations. Part II: The 2D model
2007
Abstract A novel methodology for the solution of the 2D shallow water equations is proposed. The algorithm is based on a fractional step decomposition of the original system in (1) a convective prediction, (2) a convective correction, and (3) a diffusive correction step. The convective components are solved using a Marching in Space and Time (MAST) procedure, that solves a sequence of small ODEs systems, one for each computational cell, ordered according to the cell value of a scalar approximated potential. The scalar potential is sought after computing first the minimum of a functional via the solution of a large linear system and then refining locally the optimum search. Model results are…
A Marching in Space and Time (MAST) solver of the shallow water equations. Part I: The 1D model
2007
A new approach is presented for the numerical solution of the complete 1D Saint-Venant equations. At each time step, the governing system of Partial Differential Equations (PDEs) is split, using a fractional time step methodology, into a convective prediction system and a diffusive correction system. Convective prediction system is further split into a convective prediction and a convective correction system, according to a specified approximated potential. If a scalar exact potential of the flow field exists, correction vanishes and the solution of the convective correction system is the same solution of the prediction system. Both convective prediction and correction systems are shown to …