Search results for "Runge-Kutta method"

showing 2 items of 2 documents

NUMERICAL ALGORITHMS

2013

For many systems of differential equations modeling problems in science and engineering, there are natural splittings of the right hand side into two parts, one non-stiff or mildly stiff, and the other one stiff. For such systems implicit-explicit (IMEX) integration combines an explicit scheme for the non-stiff part with an implicit scheme for the stiff part. In a recent series of papers two of the authors (Sandu and Zhang) have developed IMEX GLMs, a family of implicit-explicit schemes based on general linear methods. It has been shown that, due to their high stage order, IMEX GLMs require no additional coupling order conditions, and are not marred by order reduction. This work develops a …

General linear methodsMathematical optimizationIMEX methods; general linear methods; error analysis; order conditions; stability analysisIMEX methodsDifferential equationSCHEMESorder conditionsMathematics AppliedExtrapolationStability (learning theory)QUADRATIC STABILITYstability analysisPARABOLIC EQUATIONSSYSTEMSNORDSIECK METHODSFOS: MathematicsApplied mathematicsMathematics - Numerical AnalysisRUNGE-KUTTA METHODSMULTISTEP METHODSerror analysisMathematicsCONSTRUCTIONSeries (mathematics)Applied MathematicsNumerical analysisComputer Science - Numerical AnalysisStability analysisORDEROrder conditionsNumerical Analysis (math.NA)Computer Science::Numerical AnalysisRunge–Kutta methodsGeneral linear methodsError analysisORDINARY DIFFERENTIAL-EQUATIONSOrdinary differential equationgeneral linear methodsMathematics
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Simulation of the Propagation of Tsunamis in Coastal Regions by a Two-Dimensional Non-Hydrostatic Shallow Water Solver

2017

Due to the enormous damages and losses of human lives in the inundated regions, the simulation of the propagation of tsunamis in coastal areas has received an increasing interest of the researchers. We present a 2D depth-integrated, non- hydrostatic shallow waters solver to simulate the propagation of tsunamis, solitary waves and surges in coastal regions. We write the governing continuity and momentum equations in conservative form and discretize the domain with unstructured triangular Generalized Delaunay meshes. We apply a fractional- time-step procedure, where two problems (steps) are consecutively solved. In the first and in the second step, we hypothesize a hydrostatic and a non-hydro…

TurbulenceVoronoi cellShallow waters; Non-hydrostatic pressure; Unstructured mesh; Wetting/drying; Tsunami propagation; Long waves; Voronoi cells; Runge-Kutta method; Galerkin scheme; Manning equation; Dirichlet condition; OpenFOAMShallow waterLong waveUnstructured meshGeophysicsSolverTsunami propagationSettore ICAR/01 - IdraulicaThermal hydraulicsWetting/dryingWaves and shallow waterBoundary layerNon-hydrostatic pressureDirichlet conditionFluid dynamicsRunge-Kutta methodOpenFOAMMagnetohydrodynamicsNavier–Stokes equationsGalerkin schemeGeologyManning equation
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