Abstract
In this paper, we study a finite element discretization of a Level Set Method formulation of free-surface flow. We consider an Euler semi-implicit discretization in time and a Galerkin discretization of the level set function. We regularize the density and viscosity of the flow across the interface, following the Level Set Method. We prove stability in natural norms when the viscosity and density vary from one to the other layer and optimal error estimates for smooth solutions when the layers have the same density. We present some numerical tests for academic flows.
Funding source: Agencia Estatal de Investigación
Award Identifier / Grant number: RTI2018-093521-B-C31
Funding source: European Regional Development Fund
Award Identifier / Grant number: US-125487
Funding statement: Research partially supported by the Spanish Research Agency (AEI) and European Union FEDER project RTI2018-093521-B-C31 and by Programa Operativo FEDER Andalucía 2014–2020 Project US-125487.
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© 2021 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Robust Iterative Solvers for Gao Type Nonlinear Beam Models in Elasticity
- Using Complete Monotonicity to Deduce Local Error Estimates for Discretisations of a Multi-Term Time-Fractional Diffusion Equation
- Accurate Full-Vectorial Finite Element Method Combined with Exact Non-Reflecting Boundary Condition for Computing Guided Waves in Optical Fibers
- Robust Hybrid High-Order Method on Polytopal Meshes with Small Faces
- A Totally Relaxed, Self-Adaptive Subgradient Extragradient Method for Variational Inequality and Fixed Point Problems in a Banach Space
- Robust Discretization and Solvers for Elliptic Optimal Control Problems with Energy Regularization
- Dual System Least-Squares Finite Element Method for a Hyperbolic Problem
- Artificial Compressibility Methods for the Incompressible Navier–Stokes Equations Using Lowest-Order Face-Based Schemes on Polytopal Meshes
- Numerical Analysis of a Finite Element Approximation to a Level Set Model for Free-Surface Flows
- Inexact Inverse Subspace Iteration with Preconditioning Applied to Quadratic Matrix Polynomials
- Convergence Theory for IETI-DP Solvers for Discontinuous Galerkin Isogeometric Analysis that is Explicit in ℎ and 𝑝
- Poincaré Inequality for a Mesh-Dependent 2-Norm on Piecewise Linear Surfaces with Boundary
Artikel in diesem Heft
- Frontmatter
- Robust Iterative Solvers for Gao Type Nonlinear Beam Models in Elasticity
- Using Complete Monotonicity to Deduce Local Error Estimates for Discretisations of a Multi-Term Time-Fractional Diffusion Equation
- Accurate Full-Vectorial Finite Element Method Combined with Exact Non-Reflecting Boundary Condition for Computing Guided Waves in Optical Fibers
- Robust Hybrid High-Order Method on Polytopal Meshes with Small Faces
- A Totally Relaxed, Self-Adaptive Subgradient Extragradient Method for Variational Inequality and Fixed Point Problems in a Banach Space
- Robust Discretization and Solvers for Elliptic Optimal Control Problems with Energy Regularization
- Dual System Least-Squares Finite Element Method for a Hyperbolic Problem
- Artificial Compressibility Methods for the Incompressible Navier–Stokes Equations Using Lowest-Order Face-Based Schemes on Polytopal Meshes
- Numerical Analysis of a Finite Element Approximation to a Level Set Model for Free-Surface Flows
- Inexact Inverse Subspace Iteration with Preconditioning Applied to Quadratic Matrix Polynomials
- Convergence Theory for IETI-DP Solvers for Discontinuous Galerkin Isogeometric Analysis that is Explicit in ℎ and 𝑝
- Poincaré Inequality for a Mesh-Dependent 2-Norm on Piecewise Linear Surfaces with Boundary