An unconditionally stable artificial compression method for the time‐dependent groundwater‐surface water flows
Yi Qin, Yang Wang, Yanren Hou, Jian Li
Abstract
Abstract In this article, we propose a second order, unconditionally stable artificial compression method for the fully evolutionary Stokes/Darcy and Navier‐Stokes/Darcy equations that model the coupling surface and groundwater flows. It uncouples the surface from the groundwater flow by the Crank‐Nicolson Leapfrog scheme for the discretization in time, and through the artificial compression method without artificial pressure boundary conditions to decouple the velocity and pressure of the incompressible flow. Finally, we have verified the stability and second‐order convergence of the algorithm from theoretical analysis and numerical experiments.
Topics & Concepts
DiscretizationConvergence (economics)CompressibilityMathematicsDarcy's lawStability (learning theory)Flow (mathematics)Darcy–Weisbach equationCompression (physics)Groundwater flowBoundary value problemStokes flowApplied mathematicsMechanicsGroundwaterMathematical analysisGeotechnical engineeringGeometryComputer scienceGeologyPorous mediumPorosityAquiferThermodynamicsPhysicsMachine learningEconomic growthEconomicsAdvanced Numerical Methods in Computational MathematicsComputational Fluid Dynamics and AerodynamicsModel Reduction and Neural Networks