An historical overview of the development traffic flow models is proposed in form a model tree. The tree shows genealogy four families: fundamental relation, microscopic, mesoscopic and macroscopic models. We discuss families, branches By describing developments modeling, we take one step further back than conventional literature reviews that focus on current state-of-the-art. This allows us to identify main trends modeling: (1) convergence many generalized models, (2) adaptations extensions...

An iterative solution method, in the form of a preconditioner for Krylov subspace is presented Helmholtz equation. The based on Helmholtz-type differential operator with complex term. A multigrid iteration used approximately inverting preconditioner. choice components corresponding preconditioning matrix diagonal validated Fourier analysis. Multigrid analysis results are verified by numerical experiments. High wavenumber problems heterogeneous media solved indicating performance

Abstract Recently Eirola and Nevanlinna have proposed an iterative solution method for unsymmetric linear systems, in which the preconditioner is updated from step to step. Following their ideas we suggest variants of GMRES, a constructed per iteration by suitable approximation process, e.g., GMRES itself. Our numerical experiments indicate that this may lead considerable savings CPU‐time memory requirements typical CFD applications.

Abstract A mass‐conserving Level‐Set method to model bubbly flows is presented. The can handle high density‐ratio with complex interface topologies, such as simultaneous occurrence of bubbles and droplets. Aspects taken into account are: a sharp front (density changes abruptly), arbitrarily shaped interfaces, surface tension, buoyancy coalescence droplets/bubbles. Attention paid mass‐conservation integrity the interface. proposed computational method, where Volume‐of‐Fluid function used...

Biogrout is a new soil reinforcement method based on microbial-induced carbonate precipitation. Bacteria are placed and reactants flushed through the soil, resulting in calcium precipitation, causing an increase strength stiffness of soil. Due to this porosity decreases. The decreasing influences permeability therefore flow. To analyse process, model was created that describes process. contains concentrations dissolved species present biochemical reaction. These can be solved from...

Quantum computing technologies have become a hot topic in academia and industry receiving much attention financial support from all sides. Building quantum computer that can be used practically is itself an outstanding challenge has the 'new race to moon'. Next researchers vendors of future technologies, national authorities are showing strong interest maturing this technology due its known potential break many today's encryption techniques, which would significant potentially disruptive...

In this article we introduce new bounds on the effective condition number of deflated and preconditioned-deflated symmetric positive definite linear systems. For case a subdomain deflation such as that Nicolaides [SIAM J. Numer. Anal., 24 (1987), pp. 355--365], these theorems can provide direction in choosing proper decomposition into subdomains. If grid refinement is performed, keeping resolution fixed, insensitive to size. Subdomain very easy implement has been parallelized distributed...

Shifted Laplace preconditioners have attracted considerable attention as a technique to speed up convergence of iterative solution methods for the Helmholtz equation. In this paper we present comprehensive spectral analysis operator preconditioned with shifted Laplacian. Our is valid under general conditions. The propagating medium can be heterogeneous, and also holds different types damping, including radiation condition boundary computational domain. By combining results an upper bound on...

For various applications, it is well-known that a multi-level, in particular two-level, preconditioned CG (PCG) method an efficient for solving large and sparse linear systems with coefficient matrix symmetric positive definite. The corresponding two-level preconditioner combines traditional projection-type preconditioners to get rid of the effect both small eigenvalues matrix. In literature, PCG methods are known, coming from fields deflation, domain decomposition multigrid. Even though...

Two mismatch functions (power or current) and three coordinates (polar, Cartesian complex form) result in six versions of the Newton–Raphson method for solution power flow problems. In this paper, five new Newton developed single-phase problems our previous paper are extended to three-phase Mathematical models load, load connection, transformer, distributed generation (DG) presented. A formulation is described both current functions. Extended compared with backward-forward sweep-based...

Natural or induced fractures are typically present in subsurface geological formations. Therefore, they need to be carefully studied for reliable estimation of the long-term carbon dioxide storage. Instinctively, flow-conductive may undermine storage security as increase risk CO2 leakage if intersect plume. In addition, act flow barriers, causing significant pressure gradients over relatively small regions near fractures. Nevertheless, despite their high sensitivities, impact on full-cycle...

The development of scalable robust solvers for unstructured finite element applications related to viscous flow problems in earth sciences is an active research area. Solving high‐resolution convection with order magnitude 10 8 degrees freedom requires that scale well, respect both the number as well having optimal parallel scaling characteristics on computer clusters. We investigate use a smoothed aggregation (SA) algebraic multigrid (AMG)‐type solution strategy construct efficient...

SUMMARY This paper contains a comparison of four SIMPLE‐type methods used as solver and preconditioner for the iterative solution (Reynolds‐averaged) Navier–Stokes equations, discretized with finite volume method cell‐centered, colocated variables on unstructured grids. A matrix‐free implementation is presented, special attention given to treatment stabilization matrix maintain compact stencil suitable We find SIMPLER preconditioning be robust efficient academic test cases industrial cases....

SUMMARY Deflating the shifted Laplacian with geometric multigrid vectors yields speedup. To verify this claim, we investigate a simplified variant of Erlangga and Nabben presented in [Erlangga Nabben, ETNA, 2008;31:403–424]. We derive expressions for eigenvalues two‐level preconditioner one‐dimensional problem. These show that algorithm analyzed is not scalable. They also imaginary shift can be increased without delaying convergence outer Krylov acceleration. An increase number grid points...

Summary Dynamic two‐phase interaction of soil can be modelled by a displacement‐based, formulation. The finite element method together with semi‐implicit Euler–Cromer time‐stepping scheme renders discrete equation that solved recursion. By experience, it is found the CFL stability condition for undrained wave propagation not sufficient considered formulation to numerically stable at low values permeability. Because analysis onerous, an performed on simplified derived assuming incompressible...