A Parallel Finite-Volume Runge–Kutta Algorithm for Electromagnetic Scattering

1997 ◽  
Vol 137 (2) ◽  
pp. 299-320 ◽  
Author(s):  
Vineet Ahuja ◽  
Lyle N. Long
Keyword(s):  
Finite Volume ◽  
Electromagnetic Scattering ◽  
Runge Kutta

Advances in the Numerical Integration of the Three-Dimensional Euler Equations in Vibrating Cascades

1993 ◽  
Vol 115 (4) ◽  
pp. 781-790 ◽  
Author(s):  
G. A. Gerolymos
Keyword(s):  
Boundary Conditions ◽  
Numerical Integration ◽  
Euler Equations ◽  
Finite Volume ◽  
Three Dimensional ◽  
Computational Results ◽  
Grid Refinement ◽  
Mobile Grid ◽  
Transonic Compressor ◽  
Runge Kutta

In the present work an algorithm for the numerical integration of the three-dimensional unsteady Euler equations in vibrating transonic compressor cascades is described. The equations are discretized in finite-volume formulation in a mobile grid using isoparametric brick elements. They are integrated in time using Runge-Kutta schemes. A thorough discussion of the boundary conditions used and of their influence on results is undertaken. The influence of grid refinement on computational results is examined. Unsteady convergence of results is discussed.

An Application of Discontinuous Galerkin Method for Blast Wave Simulations

2010 ◽  
Author(s):  
Emre Alpman
Keyword(s):  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Blast Wave ◽  
Finite Volume ◽  
Discontinuous Galerkin Method ◽  
Numerical Solutions ◽  
Blast Waves ◽  
Strong Discontinuities ◽  
Runge Kutta ◽  
Volume Method

An implementation of Runge-Kutta Discontinuous Galerkin method to an in-house computational fluid dynamics code capable of simulating blast waves was performed. The resultant code was tested for two shock tube problems with moderately and extremely strong discontinuities. Numerical solutions were compared with predictions of a finite volume method and exact solutions. It was observed that when there are extreme discontinuities in the flowfield, as in the case of blast waves, the limiter adopted for solution clearly affects the overall quality of the predictions. An alternative limiting technique was proposed and tested to improve the results obtained. Blast wave predictions using Runge-Kutta Discontinuous Galerkin method with the alternative limiting technique yielded slightly stronger and faster moving shock waves compared to finite volume solutions.

scholarly journals A finite Volume Runge-Kutta Ellam Method for the Solution of Advection Diffusion Equations

2001 ◽  
Vol 6 (2) ◽  
pp. 67 ◽  
Author(s):  
Mohammed Al-Lawatia ◽  
Robert C. Sharpley ◽  
Hong Wang
Keyword(s):  
Contaminant Transport ◽  
Finite Volume ◽  
Large Time ◽  
Numerical Solutions ◽  
Standard Test ◽  
Diffusion Equations ◽  
Governing Equations ◽  
Adjoint Methods ◽  
Advection Diffusion ◽  
Runge Kutta

We develop a finite volume characteristic method for the solution of the advection-diffusion equations which model the contaminant transport through porous medium. This method uses a second order Runge-Kutta approximation for the characteristics within the framework of the Eulerian Lagrangian localized adjoint methods (ELLAM). The derived scheme conserves mass, symmetrizes the governing equations and generates accurate numerical solutions even if large time steps are used.  Numerical experiments comparing several competitive methods using a standard test example are presented to illustrate the performance of the method.  

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