SIAM Journal on Numerical Analysis · 2012 · 155 citations · 8 references
ComputingComputational EngineeringMechanical EngineeringComputational Fluid DynamicsComputational PhysicsFluid DynamicsConvergence AnalysisError EstimationFinite Difference MethodsNumerical ConvergenceNumerical Methods For Differential EquationsPressure-velocity CouplingA Posteriori Error EstimatesConvergenceDarcy - Forchheimer EquationFinite Difference DiscretizationFinite Difference GriddingFinite Difference SchemesFinite Difference Solution Of Partial Differential EquationsForchheimer Flow
A block-centered finite difference scheme is introduced to solve the nonlinear Darcy--Forchheimer equation, in which the velocity and pressure can be approximated simultaneously. The second-order error estimates for both pressure and velocity are established on a nonuniform rectangular grid. Numerical experiments using the scheme show the consistency of the convergence rates of our method with the theoretical analysis.
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