Communications in Numerical Methods in Engineering · 1993 · 31 citations · 1 references
ComputingComputational EngineeringMathematicsComputational MechanicsFinite Element AnalysisFinite Element MethodsFinite Element DiscretizationFinite Element FormulationNumerical Methods For Differential EquationsSpline CurvesTime IntegrationAdvectionAdvection-diffusion ModelsAdvection-diffusion TransportAnalytical SolutionsDiffusion EquationFinite Element ModelingNumerical DispersionNumerical Dispersion Reduction
Abstract This paper deals with the solution of the one‐dimensional advection–diffusion equation. The method of solution is based on the process‐splitting technique. The transport equation is split up into the advection part and the diffusion part at every time step. The advection transport equation is solved by a method of characteristics using a spline function for interpolation. This solution approach proves to be very effective because it reduces numerical dispersion and wiggles. The diffusion equation is solved by the standard Galerkin finite‐element method. A comparison of calculations with the results of Holly and Preissmann and with analytical solutions demonstrates the great accuracy of the proposed method.
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