Konstantin Lipnikov
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View article: Alquimia v1.0: a generic interface to biogeochemical codes – a tool for interoperable development, prototyping and benchmarking for multiphysics simulators
Alquimia v1.0: a generic interface to biogeochemical codes – a tool for interoperable development, prototyping and benchmarking for multiphysics simulators Open
Alquimia v1.0 is a generic interface to geochemical solvers that facilitates development of multiphysics simulators by enabling code coupling, prototyping and benchmarking. The interface enforces the function arguments and their types for …
View article: Analytic solutions and field-scale application for verification of coupled thermo-hydro-mechanical processes in subsurface fractured media
Analytic solutions and field-scale application for verification of coupled thermo-hydro-mechanical processes in subsurface fractured media Open
View article: Alquimia v1.0: A generic interface to biogeochemical codes – A tool for interoperable development, prototyping and benchmarking for multiphysics simulators
Alquimia v1.0: A generic interface to biogeochemical codes – A tool for interoperable development, prototyping and benchmarking for multiphysics simulators Open
We present Alquimia v1.0, a generic interface to geochemical solvers that facilitates development of multiphysics simulators by enabling code coupling, prototyping and benchmarking. The interface enforces a call signature for setting up, s…
View article: An adaptive Newton-based free-boundary Grad-Shafranov solver
An adaptive Newton-based free-boundary Grad-Shafranov solver Open
Equilibria in magnetic confinement devices result from force balancing between the Lorentz force and the plasma pressure gradient. In an axisymmetric configuration like a tokamak, such an equilibrium is described by an elliptic equation fo…
View article: A Lagrangian, discontinuous Galerkin method for 2D & 3D solid dynamics in the FLAG code
A Lagrangian, discontinuous Galerkin method for 2D & 3D solid dynamics in the FLAG code Open
View article: Extension of Finite Element methods to general polygonal (and polyhedral) meshes
Extension of Finite Element methods to general polygonal (and polyhedral) meshes Open
View article: Modeling magneto-hydrodynamics drivers and experimental loads with an ASC code (u)
Modeling magneto-hydrodynamics drivers and experimental loads with an ASC code (u) Open
View article: A framework for developing a mimetic tensor artificial viscosity for Lagrangian hydrocodes on arbitrary polygonal and polyhedral meshes (u)
A framework for developing a mimetic tensor artificial viscosity for Lagrangian hydrocodes on arbitrary polygonal and polyhedral meshes (u) Open
We construct a new mimetic tensor artificial viscosity on general polygonal and polyhedral meshes. The tensor artificial viscosity is based on a mimetic discretization of coordinate invariant operators, divergence of a tensor and gradient …
View article: Arbitrary order nodal mimetic discretizations of elliptic problems on polygonal meshes
Arbitrary order nodal mimetic discretizations of elliptic problems on polygonal meshes Open
View article: Monotonicity Conditions in the Mimetic Finite Difference Method
Monotonicity Conditions in the Mimetic Finite Difference Method Open
View article: A mimetic finite difference method for the Stokes problem with elected edge bubbles
A mimetic finite difference method for the Stokes problem with elected edge bubbles Open
A new mimetic finite difference method for the Stokes problem is proposed and analyzed. The unstable P{sub 1}-P{sub 0} discretization is stabilized by adding a small number of bubble functions to selected mesh edges. A simple strategy for …
View article: Anisotropic mesh adaptation for solution of finite element problems using hierarchical edge-based error estimates
Anisotropic mesh adaptation for solution of finite element problems using hierarchical edge-based error estimates Open
We present a new technology for generating meshes minimizing the interpolation and discretization errors or their gradients. The key element of this methodology is construction of a space metric from edge-based error estimates. For a mesh …
View article: Edge-based a posteriori error estimators for generation of d-dimensional quasi-optimal meshes
Edge-based a posteriori error estimators for generation of d-dimensional quasi-optimal meshes Open
We present a new method of metric recovery for minimization of L{sub p}-norms of the interpolation error or its gradient. The method uses edge-based a posteriori error estimates. The method is analyzed for conformal simplicial meshes in sp…
View article: Convergency analysis of the high-order mimetic finite difference method
Convergency analysis of the high-order mimetic finite difference method Open
We prove second-order convergence of the conservative variable and its flux in the high-order MFD method. The convergence results are proved for unstructured polyhedral meshes and full tensor diffusion coefficients. For the case of non-con…
View article: Applying an Oriented Divergence Theorem to Swept Face Remap
Applying an Oriented Divergence Theorem to Swept Face Remap Open
Here we present a novel oriented divergence theorem and apply the results to a swept face remap method (conservative data transfer between two meshes) in arbitrary Langrangian–Eulerian hydrodynamics. In our setting, we compute the material…
View article: A mimetic finite difference based quasi-static magnetohydrodynamic solver for force-free plasmas in tokamak disruptions
A mimetic finite difference based quasi-static magnetohydrodynamic solver for force-free plasmas in tokamak disruptions Open
Force-free plasmas are a good approximation where the plasma pressure is tiny compared with the magnetic pressure, which is the case during the cold vertical displacement event (VDE) of a major disruption in a tokamak. On time scales long …
View article: A Mimetic Finite Difference Based Quasi-Static Magnetohydrodynamic Solver for Force-Free Plasmas in Tokamak Disruptions
A Mimetic Finite Difference Based Quasi-Static Magnetohydrodynamic Solver for Force-Free Plasmas in Tokamak Disruptions Open
View article: Conservative high-order data transfer method on generalized polygonal meshes
Conservative high-order data transfer method on generalized polygonal meshes Open
View article: Multi-material swept face remapping on polyhedral meshes
Multi-material swept face remapping on polyhedral meshes Open
View article: Remapping between meshes with isoparametric cells: a case study
Remapping between meshes with isoparametric cells: a case study Open
We explore an intersection-based remap method between meshes consisting of isoparametric elements. We present algorithms for the case of serendipity isoparametric elements (QUAD8 elements) and piece-wise constant (cell-centered) discrete f…
View article: Applying an Oriented Divergence Theorem to Swept Face Remap [Slides]
Applying an Oriented Divergence Theorem to Swept Face Remap [Slides] Open
In swept remap, the source and target mesh have the same topology. Each source zone corresponds to a target zone, and each source face corresponds to a target face.
View article: Conservative remapping of material-dependent fields between possibly misaligned material regions [Slides]
Conservative remapping of material-dependent fields between possibly misaligned material regions [Slides] Open
Conclusion• algorithm to remap multi-material fields using pure material cells.• conservative even if source and target material boundaries are misaligned.• preserves linearity and local bounds if those boundaries are aligned.
View article: Conservative remapping of material-dependent fields between possibly misaligned material regions
Conservative remapping of material-dependent fields between possibly misaligned material regions Open
View article: Flow and transport in three-dimensional discrete fracture matrix models using mimetic finite difference on a conforming multi-dimensional mesh
Flow and transport in three-dimensional discrete fracture matrix models using mimetic finite difference on a conforming multi-dimensional mesh Open
View article: Reactive transport modeling for supporting climate resilience at groundwater contamination sites
Reactive transport modeling for supporting climate resilience at groundwater contamination sites Open
Climate resilience is an emerging issue at contaminated sites and hazardous waste sites, since projected climate shifts (e.g., increased/decreased precipitation) and extreme events (e.g., flooding, drought) could affect ongoing remediation…
View article: Conservative High-Order Data Transfer Method On Generalized Polygonal Meshes
Conservative High-Order Data Transfer Method On Generalized Polygonal Meshes Open
View article: <span style="font-family: monospace;">Portage</span>: A Modular Data Remap Library for Multiphysics Applications on Advanced Architectures
<span>Portage</span>: A Modular Data Remap Library for Multiphysics Applications on Advanced Architectures Open
Portage is a scalable and extensible remap library for numerical simulations. It supports state-of-the-art remap schemes for meshes and particles in 2D and 3D up to a second-order accuracy. Portage ensures critical properties such as local…
View article: Reactive Transport Modeling for Supporting Climate Resilience at Groundwater Contamination Sites
Reactive Transport Modeling for Supporting Climate Resilience at Groundwater Contamination Sites Open
Climate resilience is an emerging issue at contaminated sites and hazardous waste sites, since projected climate shifts (e.g., increased/decreased precipitation) and extreme events (e.g., flooding, drought) could affect ongoing remediation…
View article: A New Conservative Remap Method for Discontinuous Numerical Fields
A New Conservative Remap Method for Discontinuous Numerical Fields Open
Remap aims to accurately interpolate numerical fields from a source to a target mesh.It is an important component in arbitrary Lagrangian-Eulerian simulations in which the mesh evolves between time steps following the fluid displacement, a…
View article: Verification benchmarks for single-phase flow in three-dimensional fractured porous media
Verification benchmarks for single-phase flow in three-dimensional fractured porous media Open