6 citations · 8 across the 14 of their papers we have counts for
14 papers
A high-order polynomial-corrected shifted boundary method for simulating fully nonlinear water waves
Jens Visbech, Allan P. Engsig-Karup, Harry B. Bingham +1
We present a novel unfitted computational framework for simulating fully nonlinear potential flow-based water waves. Focusing on wave propagation, we describe the core methodology,…
GPU-Accelerated Energy-Conserving Methods for the Two-Dimensional Hyperbolized Serre-Green-Naghdi Equations
Collin Wittenstein, Vincent Marks, Mario Ricchiuto +1
We develop energy-conserving numerical methods for a two-dimensional hyperbolic approximation of the Serre-Green-Naghdi equations with variable bathymetry and either periodic or re…
Embedding General Conservation Constraints in Discretizations of Hyperbolic Systems on Arbitrary Meshes: A Multidimensional Framework
Rémi Abgrall, Pierre-Henri Maire, Mario Ricchiuto
The purpose of this review is to discuss the notion of conservation in hyperbolic systems and how one can formulate it at the discrete level depending on the solution representatio…
Semi-implicit strategies for the Serre-Green-Naghdi equations in hyperbolic form. Is hyperbolic relaxation really a good idea?
Emanuele Macca, Walter Boscheri, Mario Ricchiuto
The Serre-Green-Naghdi (SGN) equations provide a valuable framework for modelling fully nonlinear and weakly dispersive shallow-water flows. However, their elliptic formulation can…
Stationarity preserving nodal Finite Element methods for multi-dimensional linear hyperbolic balance laws via a Global Flux quadrature formulation
Wasilij Barsukow, Mario Ricchiuto, Davide Torlo
We consider linear, hyperbolic systems of balance laws in several space dimensions. They possess non-trivial steady states, which result from the equilibrium between derivatives of…
Genuinely multi-dimensional stationarity preserving Finite Volume formulation for nonlinear hyperbolic PDEs
Wasilij Barsukow, Mirco Ciallella, Mario Ricchiuto +1
Classical Finite Volume methods for multi-dimensional problems include stabilization (e.g.\ via a Riemann solver), that is derived by considering several one-dimensional problems i…
On general and complete multidimensional Riemann solvers for nonlinear systems of hyperbolic conservation laws
Elena Gaburro, Mario Ricchiuto, Michael Dumbser
In this work, we introduce a framework to design multidimensional Riemann solvers for nonlinear systems of hyperbolic conservation laws on general unstructured polygonal Voronoi-li…
A geometrical Green-Naghdi type system for dispersive-like waves in prismatic channels
Sergey Gavrilyuk, Mario Ricchiuto
We consider 2D free surface gravity waves in prismatic channels with bathymetric variations uniquely in the transverse direction. Starting from the Saint-Venant equations (shallow…
Structure-preserving approximations of the Serre-Green-Naghdi equations in standard and hyperbolic form
Hendrik Ranocha, Mario Ricchiuto
We develop structure-preserving numerical methods for the Serre-Green-Naghdi equations, a model for weakly dispersive free-surface waves. We consider both the classical form, requi…
Structure preserving nodal continuous Finite Elements via Global Flux quadrature
Wasilij Barsukow, Mario Ricchiuto, Davide Torlo
Numerical methods for hyperbolic PDEs require stabilization. For linear acoustics, divergence-free vector fields should remain stationary, but classical Finite Difference methods a…
Discontinuous Galerkin schemes for hyperbolic systems in non-conservative variables: quasi-conservative formulation with subcell finite volume corrections
Elena Gaburro, Walter Boscheri, Simone Chiocchetti +1
We present a novel quasi-conservative arbitrary high order accurate ADER discontinuous Galerkin (DG) method allowing to efficiently use a non-conservative form of the considered pa…
Very high order treatment of embedded curved boundaries in compressible flows: ADER discontinuous Galerkin with a space-time Reconstruction for Off-site data
Mirco Ciallella, Stephane Clain, Elena Gaburro +1
In this paper we present a novel approach for the design of high order general boundary conditions when approximating solutions of the Euler equations on domains with curved bounda…
A spectral element solution of the Poisson equation with shifted boundary polynomial corrections: influence of the surrogate to true boundary mapping and an asymptotically preserving Robin formulation
Jens Visbech, Allan Peter Engsig-Karup, Mario Ricchiuto
We present a new high-order accurate spectral element solution to the two-dimensional scalar Poisson equation subject to a general Robin boundary condition. The solution is based o…
Fully well-balanced entropy controlled discontinuous Galerkin spectral element method for shallow water flows: global flux quadrature and cell entropy correction
Yogiraj Mantri, Philipp Öffner, Mario Ricchiuto
We present a novel approach for solving the shallow water equations using a discontinuous Galerkin spectral element method. The method we propose has three main features. First, it…