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We present a dimensionally split method for solving hyperbolic conservation laws on Cartesian cut cell meshes. The approach combines local geometric and wave speed information to determine a novel stabilised cut cell flux, and we provide a…

Computational Physics · Physics 2018-03-15 Nandan Gokhale , Nikos Nikiforakis , Rupert Klein

We study the subsonic flows governed by full Euler equations in the half plane bounded below by a piecewise smooth curve asymptotically approaching x1-axis. Nonconstant conditions in the far field are prescribed to ensure the real Euler…

Analysis of PDEs · Mathematics 2007-10-22 Jun chen

In this paper we present a formally fourth-order accurate hybrid-variable method for the Euler equations in the context of method of lines. The hybrid-variable (HV) method seeks numerical approximations to both cell-averages and nodal…

Numerical Analysis · Mathematics 2023-08-22 Xianyi Zeng

Numerical methods of approximate solution of the Cauchy problem for coupled systems of evolution equations are considered. Separating simpler subproblems for individual components of the solution achieves simplification of the problem at a…

Numerical Analysis · Mathematics 2024-08-27 Petr N. Vabishchevich

A new discrete-velocity model is presented to solve the three-dimensional Euler equations. The velocities in the model are of an adaptive nature---both the origin of the discrete-velocity space and the magnitudes of the discrete-velocities…

comp-gas · Physics 2009-10-28 Balu Nadiga

Stable computational algorithms for the approximate solution of the Cauchy problem for nonstationary problems are based on implicit time approximations. Computational costs for boundary value problems for systems of coupled multidimensional…

Numerical Analysis · Mathematics 2024-03-28 P. N. Vabishchevich

The Finite Volume Method in Computational Fluid Dynamics to numerically model a fluid flow problem involves the process of formulating the numerical flux at the faces of the control volume. This process is important in deciding the…

Numerical Analysis · Mathematics 2021-08-05 Osama A. Marzouk

Nonlinear elliptic problems arise in many fields, including plasma physics, astrophysics, and optimal transport. In this article, we propose a novel operator-splitting/finite element method for solving such problems. We begin by introducing…

Numerical Analysis · Mathematics 2025-09-12 Jingyu Yang , Shingyu Leung , Jianliang Qian , Hao Liu

The Active Flux method is a numerical method for conservation laws using a combination of cell averages and point values, based on ideas from finite volumes and finite differences. This unusual mix has been shown to work well in many…

Numerical Analysis · Mathematics 2025-07-16 Wasilij Barsukow , Christian Klingenberg , Lisa Lechner , Jan Nordström , Sigrun Ortleb , Hendrik Ranocha

We show how to combine in a natural way (i.e. without any test nor switch) the conservative and non conservative formulations of an hyperbolic system that has a conservative form. This is inspired from two different class of schemes: the…

Numerical Analysis · Mathematics 2021-10-27 Rémi Abgrall

A modified HLLC-type contact preserving Riemann solver for incompressible two-phase flows using the artificial compressibility formulation is presented. Here, the density is omitted from the pressure evolution equation. Also, while…

Computational Physics · Physics 2022-07-14 Sourabh P. Bhat , J. C. Mandal

Numerical simulation of compressible fluid flows is performed using the Euler equations. They include the scalar advection equation for the density, the vector advection equation for the velocity and a given pressure dependence on the…

Computational Engineering, Finance, and Science · Computer Science 2018-01-22 Petr N. Vabishchevich

In this paper a variant of nonlinear exponential Euler scheme is proposed for solving nonlinear heat conduction problems. The method is based on nonlinear iterations where at each iteration a linear initial-value problem has to be solved.…

Numerical Analysis · Mathematics 2024-04-23 M. A. Botchev , V. T. Zhukov

In this paper, we prove the existence and uniqueness of subsonic solutions to the steady Euler flows past a smooth, axisymmetric obstacle. Specifically, for a broad class of prescribed positive axial velocities in the upstream, the subsonic…

Analysis of PDEs · Mathematics 2026-02-27 Dehua Wang , Tian-Yi Wang , Weiqiang Wang

We propose an iterative finite element method for solving non-linear hydromagnetic and steady Euler's equations. Some three-dimensional computational tests are given to confirm the convergence and the high efficiency of the method.

Numerical Analysis · Mathematics 2009-12-01 Cédric Boulbe , Tahar Zamène Boulmezaoud , T. Amari

The present paper addresses the development and implementation of the first high-order Flux Reconstruction (FR) solver for high-speed flows within the open-source COOLFluiD (Computational Object-Oriented Libraries for Fluid Dynamics)…

Computational Physics · Physics 2019-07-24 Ray Vandenhoeck , Andrea Lani

The Green's function approach of Giles and Pierce is used to build the lift and drag based analytic adjoint solutions for the two-dimensional incompressible Euler equations around irrotational base flows. The drag-based adjoint solution…

Fluid Dynamics · Physics 2023-11-22 Carlos Lozano , Jorge Ponsin

The use of limiting methods for high-order numerical approximations of hyperbolic conservation laws generally requires defining an admissible region/bounds for the solution. In this work, we present a novel approach for computing solution…

Numerical Analysis · Mathematics 2025-02-26 Tarik Dzanic , Luigi Martinelli

This paper examines an averaging technique in which the nonlinear flux term is expanded and the convective velocities are passed through a low-pass filter. It is the intent that this modification to the nonlinear flux terms will result in…

Fluid Dynamics · Physics 2009-07-02 Gregory Norgard , Kamran Mohseni

We present an advection-pressure flux-vector splitting method for the one and two- dimensional shallow water equations following the approach first proposed by Toro and V\'azquez for the compressible Euler equations. The resulting…

Numerical Analysis · Mathematics 2022-09-14 E. F. Toro , C. Castro , D. Vanzo , A. Siviglia