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1-10 of 27 reviews |
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A third-order multistep time discretization for a Chebyshev tau spectral method
Vreman A., Kuerten J. Journal of Computational Physics 304(C): 162-169, 2016. Type: Article
The authors, in a previous paper [1], noticed large errors in turbulence dissipation rate and enstrophy near the wall of a channel when solving turbulent channel flow using a spectral Chebyshev tau method in space and a Runge-Kutta (RK...
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Feb 4 2016 |
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Parameter selection and numerical approximation properties of Fourier extensions from fixed data
Adcock B., Ruan J. Journal of Computational Physics 273453-471, 2014. Type: Article
The term “Fourier extensions” refers to a technique for approximating nonsmooth or nonperiodic functions using Fourier modes. Fourier series can approximate a smooth and periodic function very well with spectral con...
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Jan 13 2015 |
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Finite volume local evolution Galerkin method for two-dimensional relativistic hydrodynamics
Wu K., Tang H. Journal of Computational Physics 256277-307, 2014. Type: Article
Wu and Tang provide a list of references detailing the various methods used for the solution of relativistic hydrodynamic equations. Some of these methods are extensions of nonrelativistic equations; most are based on one-dimensional R...
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Nov 12 2014 |
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The equilibrium state method for hyperbolic conservation laws with stiff reaction terms
Zhang B., Liu H., Chen F., Wang J. Journal of Computational Physics 263151-176, 2014. Type: Article
Zhang et al. propose a new fractional-step method for the numerical solution of advection equations with stiff source terms. In general, it is too difficult to obtain satisfactory numerical approximate solutions for stiff reaction prob...
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Oct 29 2014 |
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 Fast alternating-direction finite difference methods for three-dimensional space-fractional diffusion equations
Wang H., Du N. Journal of Computational Physics 258305-318, 2014. Type: Article
Differential equations of fractional order have in recent years proven to be very useful tools for the mathematical modeling of many phenomena in science and engineering. Certain types of behavior that can be observed in reality can on...
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Sep 12 2014 |
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Finite difference methods for the time fractional diffusion equation on non-uniform meshes
Zhang Y., Sun Z., Liao H. Journal of Computational Physics 265195-210, 2014. Type: Article
The development of numerical methods for fractional calculus is an extensive area of contemporary mathematics with various applications in semiconductors, nanophysics, plasma and thermodynamics, acoustics, and quantum optics. These lea...
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Sep 8 2014 |
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hp-multigrid as smoother algorithm for higher order discontinuous Galerkin discretizations of advection dominated flows: Part I: multilevel analysis
Van Der Vegt J., Rhebergen S. Journal of Computational Physics 231(22): 7537-7563, 2012. Type: Article
Understanding multidimensional decaying turbulent flows, advection-dominated flows, and convection-diffusion models requires the integration of accurate numerical structures, techniques, and simulated solutions. The choice of mathemati...
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Feb 11 2013 |
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Efficient low-storage Runge-Kutta schemes with optimized stability regions
Niegemann J., Diehl R., Busch K. Journal of Computational Physics 231(2): 364-372, 2012. Type: Article
“New low-storage Runge-Kutta schemes with optimized stability regions [designed especially] for advection-dominated problems” are proposed in this paper. The methods are proved to be well suited for the case of appl...
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Apr 5 2012 |
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Dimension reduction method for ODE fluid models
Tartakovsky A., Panchenko A., Ferris K. Journal of Computational Physics 230(23): 8554-8572, 2011. Type: Article
Numerical solutions of time-dependent partial differential equations (PDEs) lead to a system of ordinary differential equations (ODEs). To improve the accuracy, one requires a mesh refinement that will result in an increase in the dime...
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Feb 23 2012 |
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A quasi-optimal non-overlapping domain decomposition algorithm for the Helmholtz equation
Boubendir Y., Antoine X., Geuzaine C. Journal of Computational Physics 231(2): 262-280, 2012. Type: Article
The numerical solution of partial differential equations is one of the prime tasks in scientific computing. The two most important challenges in this area are the increasing size of the models and the ever-stricter accuracy requirement...
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Feb 8 2012 |
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