1,720,975 research outputs found
A semi-implicit, semi-Lagrangian, p-adaptive discontinuous Galerkin method for the shallow water equations
No full textA semi-Lagrangian Discontinuous Galerkin Method for Scalar Advection by Incompressible Flows
No full textA new, conservative semi-Lagrangian formulation is proposed for the discretization of the scalar advection equation in
flux form. The approach combines the accuracy and conservation properties of the Discontinuous Galerkin (DG) method
with the computational efficiency and robustness of Semi-Lagrangian (SL) techniques. Unconditional stability in the von
Neumann sense is proved for the proposed discretization in the one-dimensional case. A monotonization technique is then
introduced, based on the Flux Corrected Transport approach. This yields a multi-dimensional monotonic scheme for the
piecewise constant component of the computed solution that is characterized by a smaller amount of numerical diffusion
than standard DG methods. The accuracy and stability of the method are further demonstrated by two-dimensional tracer
advection tests in the case of incompressible flows. The comparison with results obtained by standard SL and DG methods
highlights several advantages of the new technique
A study of spectral element and discontinuous Galerkin methods for the Navier-Stokes equations in nonhydrostatic mesoscale atmospheric modeling: Equation sets and test cases
Full text linkThe article of record as published may be located at http://dx.doi.org/10.1016/j.jcp.2007.12.009We present spectral element (SE) and discontinuous Galerkin (DG) solutions of the Euler and compressible Navier-Stokes (NS) equations for stratified fluid flow which are of importance in nonhydrostatic mesoscale atmospheric modeling. We study three different forms of the governing equations using seven test cases. Three test cases involve flow over mountains which require the implementation of non-reflecting boundary conditions, while one test requires viscous terms (density current). Including viscous stresses into finite difference, finite element, or spectral element models poses no additional challenges; however, including these terms to either finite volume or discontinuous Galerkin models requires the introduction of additional machinery because these methods were originally designed for first-order operators. We use the local discontinuous Galerkin method to overcome this obstacle. The seven test cases show that all of our models yield good results. The main conclusion is that equation set 1 (non-conservation form) does not perform as well as sets 2 and 3 (conservation forms). For the density current (viscous), the SE and DG models using set 3 (mass and total energy) give less dissipative results than the other equation sets; based on these results we recommend set 3 for the development of future multiscale research codes. In addition, the fact that set 3 conserves both mass and energy up to machine precision motives us to pursue this equation set for the development of future mesoscale models. For the bubble and mountain tests, the DG models performed better. Based on these results and due to its conservation properties we recommend the DG method. In the worst case scenario, the DG models are 50% slower than the non-conservative SE models. In the best case scenario, the DG models are just as efficient as the conservative SE models
High-order semi-implicit time-integrators for a triangular discontinuous Galerkin oceanic shallow water model
Full text linkThe Discontinuous Galerkin Coastal Ocean Model (DGCOM) is a two-dimensional shallow water model for simulating coastal ocean processes.The article of record may be found at http://www.doi.org/10.1002/fld.2118We extend the explicit in time high-order triangular discontinuous Galerkin (DG) method to semi-implicit (SI) and then apply the algorithm to the two-dimensional oceanic shallow water equations; we implement high-order SI time-integrators using the backward difference formulas from orders one to six. The reason for changing the time-integration method from explicit to SI is that explicit methods require a very small time step in order to maintain stability, especially for high-order DG methods. Changing the time- integration method to SI allows one to circumvent the stability criterion due to the gravity waves, which for most shallow water applications are the fastest waves in the system (the exception being supercritical flow where the Froude number is greater than one). The challenge of constructing a SI method for a DG model is that the DG machinery requires not only the standard finite element-type area integrals, but also the finite volume-type boundary integrals as well. These boundary integrals pose the biggest challenge in a SI discretization because they require the construction of a Riemann solver that is the true linear representation of the nonlinear Riemann problem; if this condition is not satisfied then the resulting numerical method will not be consistent with the continuous equations. In this paper we couple the SI time-integrators with the DG method while maintaining most of the usual attributes associated with DG methods such as: high-order accuracy (in both space and time), parallel efficiency, excellent stability, and conservation. The only property lost is that of a compact communication stencil typical of time-explicit DG methods; implicit methods will always require a much larger communication stencil. We apply the new high-order SI DG method to the shallow water equations and show results for many standard test cases of oceanic interest such as: standing, Kelvin and Rossby soliton waves, and the Stommel problem. The results show that the new high-order SI DG model, that has already been shown to yield exponentially convergent solutions in space for smooth problems, results in a more efficient model than its explicit counterpart. Furthermore, for those problems where the spatial resolution is sufficiently high compared with the length scales of the flow, the capacity to use high-order (HO) time-integrators is a necessary complement to the employment of HO space discretizations, since the total numerical error would be otherwise dominated by the time discretization error. In fact, in the limit of increasing spatial resolution, it makes little sense to use HO spatial discretizations coupled with low-order time discretizations
A simulation system based on mixed-hybrid finite elementsfor thermal oxidation in semiconductor technology
No full textSemi-Implicit Formulations of the Navier--Stokes Equations: Application to Nonhydrostatic Atmospheric Modeling
Full text linkThe article of record as published may be located at http://dx.doi.org/10.1137/090775889We present semi-implicit (implicit-explicit) formulations of the compressible NavierﾖStokes equations (NSE) for applications in nonhydrostatic atmospheric modeling. The compressible
NSE in nonhydrostatic atmospheric modeling include buoyancy terms that require special handling if one wishes to extract the Schur complement form of the linear implicit problem. We present results for five different forms of the compressible NSE and describe in detail how to formulate the semi-implicit time-integration method for these equations. Finally, we compare all five equations and compare the semi-implicit formulations of these equations both using the Schur and No Schur forms against an explicit RungeﾖKutta method. Our simulations show that, if efficiency is the main criterion, it matters which form of the governing equations you choose. Furthermore, the semi-implicit formulations are faster than the explicit RungeﾖKutta method for all the tests studied, especially if the Schur form is used. While we have used the spectral element method for discretizing the spatial operators, the semi-implicit formulations that we derive are directly applicable to all other numerical methods. We show results for our five semi-implicit models for a variety of problems of interest in nonhydrostatic atmospheric modeling, including inertia-gravity waves, density current (i.e., KelvinﾖHelmholtz instabilities), and mountain test cases; the latter test case requires the implementation of nonreflecting boundary conditions. Therefore, we show results for all five semi-implicit models using the appropriate boundary conditions required in nonhydrostatic atmospheric modeling: no-flux (reflecting) and nonreflecting boundary conditions (NRBCs). It is shown that the NRBCs exert a
strong impact on the accuracy and efficiency of the models
A conservative discontinuous Galerkin semi-implicit formulation for the Navier-Stokes equations in nonhydrostatic mesoscale modeling
Full text linkNon-hydrostatic Unified Model of the Atmosphere (NUMA)The first NUMA papers appeared in 2008. From 2008 through 2010, all the NUMA papers appearing involved the 2D (x-z slice) Euler equations. All the theory and numerical implementations were first developed in 2D.The article of record may be found at http://dx.doi.org/10.1137/070708470A discontinuous Galerkin (DG) finite element formulation is proposed for the solu- tion of the compressible Navier–Stokes equations for a vertically stratified fluid, which are of interest in mesoscale nonhydrostatic atmospheric modeling. The resulting scheme naturally ensures con- servation of mass, momentum, and energy. A semi-implicit time-integration approach is adopted to improve the efficiency of the scheme with respect to the explicit Runge–Kutta time integration strategies usually employed in the context of DG formulations. A method is also presented to refor- mulate the resulting linear system as a pseudo-Helmholtz problem. In doing this, we obtain a DG discretization closely related to those proposed for the solution of elliptic problems, and we show how to take advantage of the numerical integration rules (required in all DG methods for the area and flux integrals) to increase the efficiency of the solution algorithm. The resulting numerical for- mulation is then validated on a collection of classical two-dimensional test cases, including density driven flows and mountain wave simulations. The performance analysis shows that the semi-implicit method is, indeed, superior to explicit methods and that the pseudo-Helmholtz formulation yields further efficiency improvements
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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