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An isogeometric boundary element method for problems in elasticity is presented, which is based on an independent approximation for the geometry, traction and displacement field. This enables a flexible choice of refinement strategies,…

Numerical Analysis · Computer Science 2015-02-04 Benjamin Marussig , Jürgen Zechner , Gernot Beer , Thomas-Peter Fries

The computational cost of the boundary-condition-enforced immersed boundary method (IBM) increases in the order of $\mathcal{O}(N^2)$ as the number of Lagrangian points, $N$, increases. This is due to the time-consuming calculation of the…

Fluid Dynamics · Physics 2024-03-25 Manabu Saito , Ryoichi Kurose

This paper proposes the first free-stream boundary condition in a purely Lagrangian framework for weakly-compressible smoothed particle hydrodynamics (WCSPH). The boundary condition is implemented based on several numerical techniques,…

Fluid Dynamics · Physics 2023-07-04 Shuoguo Zhang , Wenbin Zhang , Chi Zhang , Xiangyu Hu

The problem of increasing the accuracy of an approximate solution is considered for boundary value problems for parabolic equations. For ordinary differential equations (ODEs), nonstandard finite difference schemes are in common use for…

Numerical Analysis · Computer Science 2017-05-22 Petr N. Vabishchevich

In this paper, we propose a review of the free boundary formulation for BVPs defined on semi-infinite intervals. The main idea and theorem are illustrated, for the reader convenience, by using a class of second-order BVPs. Moreover, we are…

Numerical Analysis · Mathematics 2020-11-17 Riccardo Fazio

In numerical ocean models coast lines change the direction from one grid cell to its neighbor and the value for viscosity is set to be as small as possible. Therefore, model simulations are not converged with resolution and boundary…

Fluid Dynamics · Physics 2015-07-14 Peter D. Düben , Peter Korn

We propose an enhanced wall-boundary treatment for the lattice Boltzmann method (LBM), designed for high-Reynolds-number turbulent flows on adaptively refined Cartesian grids. The method improves the slip-velocity bounce-back scheme by…

Fluid Dynamics · Physics 2026-01-27 Jorge Ponsin , Carlos Lozano

An algorithm for a family of self-starting high-order implicit time integration schemes with controllable numerical dissipation is proposed for both linear and nonlinear transient problems. This work builds on the previous works of the…

Numerical Analysis · Mathematics 2024-09-23 Daniel O'Shea , Xiaoran Zhang , Shayan Mohammadian , Chongmin Song

In this work we study the dynamic behaviour of compound shells of revolution partially filled with an ideal incompressible fluid based on boundary-value problems. New analytical mathematical model with corresponding discrete scheme for the…

Computational Engineering, Finance, and Science · Computer Science 2016-06-15 Iryna Kononenko , Oleksiy Kononenko

This work proposes an efficient space-time two-grid compact difference (ST-TGCD) scheme for solving the two-dimensional (2D) viscous Burgers' equation subject to initial and periodic boundary conditions. The proposed approach combines a…

Numerical Analysis · Mathematics 2025-10-20 Xiangyi Peng , Lisen Ding , Wenlin Qiu

This paper presents a novel spline-based meshing technique that allows for usage of boundary-conforming meshes for unsteady flow and temperature simulations in co-rotating twin-screw extruders. Spline-based descriptions of arbitrary screw…

Numerical Analysis · Mathematics 2020-02-19 Jochen Hinz , Jan Helmig , Matthias Möller , Stefanie Elgeti

In this paper two new families of arbitrary high order accurate spectral DG finite element methods are derived on staggered Cartesian grids for the solution of the inc.NS equations in two and three space dimensions. Pressure and velocity…

Numerical Analysis · Mathematics 2016-12-06 Francesco Fambri , Michael Dumbser

This paper presents a spatial two-grid (STG) compact difference scheme for a two-dimensional (2D) nonlinear diffusion-wave equation with variable exponent, which describes, e.g., the propagation of mechanical diffusive waves in viscoelastic…

Numerical Analysis · Mathematics 2025-10-15 Hao Zhang , Kexin Li , Wenlin Qiu

We perform a numerical free evolution of a selfgravitating, spherically symmetric scalar field satisfying the wave equation. The evolution equations can be written in a very simple form and are symmetric hyperbolic in Eddington-Finkelstein…

General Relativity and Quantum Cosmology · Physics 2009-11-07 Mirta S. Iriondo , Oscar A. Reula

Immersed boundary methods simplify mesh generation by embedding the domain of interest into an extended domain that is easy to mesh, introducing the challenge of dealing with cells that intersect the domain boundary. Combined with explicit…

Computational Engineering, Finance, and Science · Computer Science 2026-01-13 Christian Faßbender , Tim Bürchner , Philipp Kopp , Ernst Rank , Stefan Kollmannsberger

Embedding geometries in structured grids allows a simple treatment of complex objects in fluid simulations. Various methods for embedding geometries are available. The commonly used Brinkman-volume-penalization models geometries as porous…

Fluid Dynamics · Physics 2021-11-17 Julius Reiss

We develop an efficient numerical method for calculating the image stress field induced by spherical voids in materials. The method is applied to dislocation-void interactions in dislocation dynamics simulations. We obtain a complete set of…

Computational Physics · Physics 2019-02-14 Yifan Wang , Xiaohan Zhang , Wei Cai

We present a novel framework inspired by the Immersed Boundary Method for predicting the fluid-structure interaction of complex structures immersed in flows with moderate to high Reynolds numbers. The main novelties of the proposed…

We develop a general strategy in order to implement (approximate) discrete transparent boundary conditions for finite difference approximations of the two-dimensional transport equation. The computational domain is a rectangle equipped with…

Analysis of PDEs · Mathematics 2019-09-12 Christophe Besse , Jean-François Coulombel , Pascal Noble

We prove the well--posedness of a dynamical perfect plasticity model under general assumptions on the stress constraint set and on the reference configuration. The problem is studied by combining both calculus of variations and hyperbolic…

Analysis of PDEs · Mathematics 2019-12-13 Jean-François Babadjian , Vito Crismale