NUMERICAL STUDIES OF CONJUGATED INFINITE ELEMENTS FOR ACOUSTICAL RADIATION

2000 ◽  
Vol 08 (01) ◽  
pp. 1-24 ◽  
Author(s):  
R. J. ASTLEY ◽  
J. A. HAMILTON
Keyword(s):  
Implicit Time ◽  
Variable Order ◽  
Shape Functions ◽  
Infinite Elements ◽  
Time Stepping ◽  
Oblate Spheroidal ◽  
Numerical Studies ◽  
Transient Solutions ◽  
Wave Problems ◽  
Spheroidal Coordinates

Aspects of conjugated infinite element schemes for unbounded wave problems are reviewed and a general formulation is presented for elements of variable order based on separable shape functions expressed in terms of prolate and oblate spheroidal coordinates. The formulation encompasses both "conjugated Burnett" and "Astley–Leis" elements. The performance of the two approaches is compared for steady multipole wave fields and the effect of the radial basis on the condition number of the resulting equations is discussed. Transient formulations based on these elements are derived and methods for solving the resulting transient equations are discussed. The use of an implicit time stepping scheme coupled with an indirect iterative solver is shown to give fast transient solutions which do not require matrix inversion.

scholarly journals Well-posedness and numerical approximation of a fractional diffusion equation with a nonlinear variable order

2020 ◽  
Author(s):  
Buyang Li ◽  
Hong Wang ◽  
Jilu Wang
Keyword(s):  
Numerical Solutions ◽  
Fractional Diffusion ◽  
Regularity Of Solutions ◽  
Implicit Time ◽  
Variable Order ◽  
Well Posedness ◽  
Rigorous Analysis ◽  
Time Stepping ◽  
Regularity Results ◽  
Unknown Solution

We prove well-posedness and regularity of solutions to a fractional diffusion porous media equation with a variable order that may depend on the unknown solution. We present a linearly implicit time-stepping method to linearize and discretize the equation in time, and present rigorous analysis for the convergence of numerical solutions based on proved regularity results.

A Numerical Model of In-Channel Pebble Bed Thermal Storage for a Solar Chimney

2012 ◽  
Author(s):  
Brandon Schulte ◽  
O. A. Plumb
Keyword(s):  
Numerical Model ◽  
Present Model ◽  
Thermal Storage ◽  
Implicit Time ◽  
Heat Transfer Characteristics ◽  
Solar Chimney ◽  
Pebble Bed ◽  
One Dimensional ◽  
Time Stepping ◽  
Daily Energy

In this study, solar chimney performance is numerically modeled. Previously published models have considered water bags and natural earth as means to store daytime thermal energy for nighttime operation of the system. The present model considers in-channel pebble bed thermal storage. A one-dimensional, implicit time stepping numerical model is developed to predict solar chimney performance throughout a 24 hour period. The model is partially verified with available experimental data. The daily energy, daily efficiency and heat transfer characteristics of the solar chimney with pebble bed thermal storage are summarized. The numerical simulation showed that by introducing a pebble bed, nightly exit velocities reach 40% of the peak daytime velocity. However, the daily kinetic energy delivered by a solar chimney with pebble bed thermal storage is much less than a traditional solar chimney, suggesting pebble bed thermal storage is more practicable in building heating applications as opposed to power generation.

Torsional oscillation of a homogeneous elastic spheroid

1962 ◽  
Vol 52 (3) ◽  
pp. 469-484 ◽  
Author(s):  
Tatsuo Usami ◽  
Yasuo Satô
Keyword(s):  
Fundamental Mode ◽  
Free Oscillation ◽  
Torsional Oscillation ◽  
Numerical Calculations ◽  
Higher Harmonics ◽  
Oblate Spheroidal ◽  
The Earth ◽  
Spectral Peaks ◽  
The Difference ◽  
Spheroidal Coordinates

abstract There are several causes for the observations of splitting of the spectral peaks determined from the free oscillation of the earth. In this paper, the splitting due to the ellipticity is studied assuming a homogeneous earth described by oblate spheroidal coordinates. Ellipticity causes the iTn mode to split into (n + 1) modes, while the earth's rotation causes it to split into (2n + 1) modes. 1/297.0 is adopted as the ellipticity of the earth. Numerical calculations are carried out for the fundamental mode (n = 2, 3, 4) and for the first higher harmonics (n = 1). The difference between the extreme frequencies for each value of n is 0.7% (n = 2), 0.5% (n = 3), and 0.4% (n = 4).

scholarly journals FVM 1.0: a nonhydrostatic finite-volume dynamical core for the IFS

2019 ◽  
Vol 12 (2) ◽  
pp. 651-676 ◽  
Author(s):  
Christian Kühnlein ◽  
Willem Deconinck ◽  
Rupert Klein ◽  
Sylvie Malardel ◽  
Zbigniew P. Piotrowski ◽  
...  
Keyword(s):  
Finite Volume ◽  
Numerical Weather Prediction ◽  
Weather Prediction ◽  
Implicit Time ◽  
Integration Scheme ◽  
Advective Transport ◽  
Numerical Weather ◽  
Time Stepping ◽  
Spectral Transform ◽  
Volume Integration

Abstract. We present a nonhydrostatic finite-volume global atmospheric model formulation for numerical weather prediction with the Integrated Forecasting System (IFS) at ECMWF and compare it to the established operational spectral-transform formulation. The novel Finite-Volume Module of the IFS (henceforth IFS-FVM) integrates the fully compressible equations using semi-implicit time stepping and non-oscillatory forward-in-time (NFT) Eulerian advection, whereas the spectral-transform IFS solves the hydrostatic primitive equations (optionally the fully compressible equations) using a semi-implicit semi-Lagrangian scheme. The IFS-FVM complements the spectral-transform counterpart by means of the finite-volume discretization with a local low-volume communication footprint, fully conservative and monotone advective transport, all-scale deep-atmosphere fully compressible equations in a generalized height-based vertical coordinate, and flexible horizontal meshes. Nevertheless, both the finite-volume and spectral-transform formulations can share the same quasi-uniform horizontal grid with co-located arrangement of variables, geospherical longitude–latitude coordinates, and physics parameterizations, thereby facilitating their comparison, coexistence, and combination in the IFS. We highlight the advanced semi-implicit NFT finite-volume integration of the fully compressible equations of IFS-FVM considering comprehensive moist-precipitating dynamics with coupling to the IFS cloud parameterization by means of a generic interface. These developments – including a new horizontal–vertical split NFT MPDATA advective transport scheme, variable time stepping, effective preconditioning of the elliptic Helmholtz solver in the semi-implicit scheme, and a computationally efficient implementation of the median-dual finite-volume approach – provide a basis for the efficacy of IFS-FVM and its application in global numerical weather prediction. Here, numerical experiments focus on relevant dry and moist-precipitating baroclinic instability at various resolutions. We show that the presented semi-implicit NFT finite-volume integration scheme on co-located meshes of IFS-FVM can provide highly competitive solution quality and computational performance to the proven semi-implicit semi-Lagrangian integration scheme of the spectral-transform IFS.

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