Related papers: Westervelt Equation Simulation on Manifold using D…
The classical numerical methods play important roles in solving wave equation, e.g. finite difference time domain method. However, their computational domain are limited to flat space and the time. This paper deals with the description of…
In this paper, the method of discrete exterior calculus for numerically solving Maxwell's equations in space manifold and the time is discussed, which is a kind of lattice gauge theory. The analysis of its stable condition and error is also…
Westervelt's equation is a nonlinear wave equation that is widely used to model the propagation of sound waves in a compressible medium, with one important application being ultra-sound in human tissue. Two fundamental aspects of this…
Efficient time integration methods based on operator splitting are introduced for the Westervelt equation, a nonlinear damped wave equation that arises in nonlinear acoustics as mathematical model for the propagation of sound waves in high…
In this paper, we study the nonlinear periodic Westervelt equation with excitations located within a bounded domain in $\mathbb{R}^d$, where $d \in \{2,3\}$, subject to Robin boundary conditions. This problem is of particular interest for…
Maxwell's equations can be solved numerically in space manifold and the time by discrete exterior calculus as a kind of lattice gauge theory.Since the stable conditions of this method is very severe restriction, we combine the implicit…
A form of the conservation equations for fluid dynamics is presented, deduced using slightly less restrictive hypothesis than those necessary to obtain the Westervelt equation. This formulation accounts for full wave diffraction,…
This paper addresses the numerical solution of the Westervelt equation, which arises as one of the model equations in nonlinear acoustics. The problem is rewritten in a canonical form that allows the systematic discretization by Galerkin…
We propose a self-adaptive absorbing technique for quasilinear ultrasound waves in two- and three-dimensional computational domains. As a model for the nonlinear ultrasound propagation in thermoviscous fluids, we employ Westervelt's wave…
Nonlinear distortion of infrasonic waves through atmospheres up to thermospheric altitudes govern large-range ground-level observations of explosive noise sources, causing large differences between the near and far field. Propagation…
We propose and analyze a space-time finite element method for Westervelt's quasilinear model of ultrasound waves in second-order formulation. The method combines conforming finite element spatial discretizations with a…
We develop a numerical method for the Westervelt equation, an important equation in nonlinear acoustics, in the form where the attenuation is represented by a class of non-local in time operators. A semi-discretisation in time based on the…
We present an explicit finite difference time domain method to solve the lossless Westervelt equation for a moving wave emitting boundary in one dimension and in spherical symmetry. The approach is based on a coordinate transformation…
The Westervelt equation describes the propagation of pressure waves in continuous nonlinear and, eventually, diffusive media. The classical framework of this equation corresponds to fluid dynamics theory. This work seeks to connect this…
In this paper we show local (and partially global) in time existence for the Westervelt equation with several versions of nonlinear damping. This enables us to prove well-posedness with spatially varying $L_\infty$-coefficients, which…
Harmonic generation plays a crucial role in contrast-enhanced ultrasound, both for imaging and therapeutic applications. However, accurately capturing these nonlinear effects is computationally very demanding when using traditional…
The focus of this work is on the construction of a family of nonlinear absorbing boundary conditions for the Westervelt equation in one and two space dimensions. The principal ingredient used in the design of such conditions is…
Motivated by numerical modeling of ultrasound waves, we investigate robust conforming finite element discretizations of quasilinear and possibly nonlocal equations of Westervelt type. These wave equations involve either a strong dissipation…
We investigate a nonlinear multiphysics model motivated by ultrasound-enhanced drug delivery. The acoustic pressure field is modeled by Westervelt's quasilinear wave equation to adequately capture the nonlinear effects in ultrasound…
To predict the heat diffusion in a given region over time, it is often necessary to find the numerical solution for heat equation. With the techniques of discrete differential calculus, we propose two unconditional stable numerical schemes…