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State redistribution (SRD) is a recently developed technique for stabilizing cut cells that result from finite-volume embedded boundary methods. SRD has been successfully applied to a variety of compressible and incompressible flow…
State redistribution is an algorithm that stabilizes cut cells for embedded boundary grid methods. This work extends the earlier algorithm in several important ways. First, state redistribution is extended to three spatial dimensions.…
We propose an extension of the discretization approaches for multilayer shallow water models, aimed at making them more flexible and efficient for realistic applications to coastal flows. A novel discretization approach is proposed, in…
In this paper we develop a new technique, called \textit{state redistribution}, that allows the use of explicit time stepping when approximating solutions to hyperbolic conservation laws on embedded boundary grids. State redistribution is a…
We apply the cell merging method to a model shallow water problem with a permeable boundary. We use a cut cell approach which is more easily and systematically scalable with different shapes of boundaries. The novel cell merging method…
Many astrophysical systems can only be accurately modelled when the behaviour of their baryonic gas components is well understood. The residual distribution (RD) family of partial differential equation (PDE) solvers produce approximate…
A numerical method is proposed for solving the two layer shallow water equations with variable bathymetry in one dimension based on high-resolution f-wave-propagation finite volume methods. The method splits the jump in the fluxes and…
Coastal erosion describes the displacement of land caused by destructive sea waves, currents or tides. Major efforts have been made to mitigate these effects using groynes, breakwaters and various other structures. We address this problem…
We propose a state redistribution method for high order discontinuous Galerkin methods on curvilinear embedded boundary grids. State redistribution relaxes the overly restrictive CFL condition that results from arbitrarily small cut cells…
We propose an efficient algorithm for the immersed boundary method on distributed-memory architectures, with the computational complexity of a completely explicit method and excellent parallel scaling. The algorithm utilizes the…
Coastal erosion describes the displacement of land caused by destructive sea waves, currents or tides. Major efforts have been made to mitigate these effects using groins, breakwaters and various other structures. We try to address this…
In the present manuscript, we consider the problem of dispersive wave simulation on a rotating globally spherical geometry. In this Part IV, we focus on numerical aspects while the model derivation was described in Part III. The algorithm…
This paper presents a more stable implementation and a highly accurate numerical tool for predicting flooding in urban areas. We started with the (linearised) well-posedness analysis by [1], where far-field boundary conditions were proposed…
In this paper a numerical procedure to simulate low diffusivity scalar turbulence is presented. The method consists of using a grid for the advected scalar with a higher spatial resolutions than that of the momentum. The latter usually…
The paper is concerned with modeling and simulating approaches of wall distance functions based on Partial Differential Equations (PDE). The distance to the nearest wall is required for many industrial problems in Computational Fluid…
We develop numerical methods to simulate the fluid-mechanical erosion of many bodies in two-dimensional Stokes flow. The broad aim is to simulate the erosion of a porous medium (e.g. groundwater flow) with grain-scale resolution. Our fluid…
Immersed boundary methods are extensively used for simulations of dynamic solid objects interacting with fluids due to their computational efficiency and modelling flexibility compared to body-fitted grid methods. However, thin geometries,…
Simulating infiltration in porous media using Richards' equation remains computationally challenging due to its parabolic structure and nonlinear coefficients. While a wide range of numerical methods for differential equations have been…
The capability to accurately predict flood flows via numerical simulations is a key component of contemporary flood risk management practice. However, modern flood models lack the capacity to accurately model flow interactions with linear…
Modeling the effect of complex terrain on high Reynolds number flows is important to improve our understanding of flow dynamics in wind farms and the dispersion of pollen and pollutants in hilly or mountainous terrain as well as the flow in…