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Compact Schemes for Multiscale Flows with Cell-Centered Finite Difference Method
High-order compact interpolation schemes appropriate for multiscale flows are studied within a cell-centered finite difference method (CCFDM)...
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Free and Interfacial Boundaries in Individual-Based Models of Multicellular Biological systems
Coordination of cell behaviour is key to a myriad of biological processes including tissue morphogenesis, wound healing, and tumour growth. As such,...
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Implicit finite volume method with a posteriori limiting for transport networks
Simulating the flow of water in district heating networks requires numerical methods which are independent of the CFL condition. We develop a high...
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A Review of Cartesian Grid Active Flux Methods for Hyperbolic Conservation Laws
In 2011, Eymann and Roe introduced a new class of truly multidimensional finite volume methods. These so-called Active Flux methods use concepts,...
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On the impact of heterogeneity-aware mesh partitioning and non-contributing computation removal on parallel reservoir simulations
Parallel computations have become standard practice for simulating the complicated multi-phase flow in a petroleum reservoir. Increasingly...
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Monotonicity Considerations for Stabilized DG Cut Cell Schemes for the Unsteady Advection Equation
For solving unsteady hyperbolic conservation laws on cut cell meshes, the so called small cell problem is a big issue: one would like to use a time...
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An Immersed Boundary Method on Cartesian Adaptive Grids for the Simulation of Compressible Flows
In this article, we present an immersed boundary method (IBM) for the simulation of compressible flows encountered in aerodynamics. The immersed...
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The Unfitted HHO Method for the Stokes Problem on Curved Domains
We design a hybrid high-order (HHO) method to approximate the Stokes problem on curved domains using unfitted meshes. We prove inf-sup stability and...
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Ordinary Differential Equations
In this chapter, we use difference matrices to solve ordinary differential equations. We first apply Newton’s method to a second-order elliptic...
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Efficient KD-Tree Based Mesh Redistribution for Data Remap** Algorithms
In this paper, we present a new mesh redistribution algorithm developed for the parallel data remap** library Portage. During distributed memory...
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Investigation of Wave Phenomena During the Seismic Survey in the Permafrost Areas Using Two Approaches to Numerical Modeling
AbstractIn the recent years the Arctic onshore and offshore areas has become the region of interest. In the cold conditions, inhomogeneous permafrost...
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A mathematical model for cell-induced gel contraction incorporating osmotic effects
Biological tissues are composed of cells surrounded by the extracellular matrix (ECM). The ECM can be thought of as a fibrous polymer network, acting...
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Characteristic Based Volume Penalization Method for Numerical Simulation of Compressible Flows on Unstructured Meshes
AbstractA characteristic based volume penalization method for numerical simulation of viscous compressible gas flows near solid bodies with immersed...
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An Unfitted Finite Element Method by Direct Extension for Elliptic Problems on Domains with Curved Boundaries and Interfaces
We propose and analyze an unfitted finite element method of arbitrary order for solving elliptic problems on domains with curved boundaries and...
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An efficient scenario penalization matheuristic for a stochastic scheduling problem
We propose a new scenario penalization matheuristic for a stochastic scheduling problem based on both mathematical programming models and local...
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Stable Second Order Boundary Conditions for Kinetic Approximations
WeHélie, Romane introduceHelluy, Philippe a general framework for applying boundary conditions in the vectorial kinetic scheme of Bouchut [2, 4]. The...
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Eulerian time-step** schemes for the non-stationary Stokes equations on time-dependent domains
This article is concerned with the discretisation of the Stokes equations on time-dependent domains in an Eulerian coordinate framework. Our work can...
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A Method to Solve Hamilton–Jacobi Type Equation on Unstructured Meshes
A new method is developed to approximate a first-order Hamilton–Jacobi equation. The constant motion of an interface in the normal direction is of...
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Discontinuous Galerkin Method with an Entropic Slope Limiter for Euler Equations
AbstractThe variational approach to obtaining equations of the entropy stable discontinuous Galerkin method is generalized. It is shown how the...
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Advanced Topics in Semilinear Elliptic BVP
We lightly introduce a few more advanced topics concerning semilinear elliptic BVP. In particular, we introduce four algorithms for finding solutions...