Related papers: New Low-Dissipation Central-Upwind Schemes. Part I…
We introduce new second-order adaptive low-dissipation central-upwind (LDCU) schemes for the one- and two-dimensional hyperbolic systems of conservation laws. The new adaptive LDCU schemes employ the LDCU numerical fluxes (recently proposed…
We introduce second-order low-dissipation (LD) path-conservative central-upwind (PCCU) schemes for the one- (1-D) and two-dimensional (2-D) multifluid systems, whose components are assumed to be immiscible and separated by material…
Central schemes for conservation laws are Riemann solver free methods which are simple and easy to implement. In recent work for Euler equations [Kurganov & Xin, J. Sci. Comput., 96:56, 2023] their accuracy has been enhanced in terms of…
We develop a new second-order unstaggered path-conservative central-upwind (PCCU) scheme for ideal and shallow water magnetohydrodynamics (MHD) equations. The new scheme possesses several important properties: it locally preserves the…
This work provides a comparative assessment of several low-dissipation numerical schemes for hyperbolic conservation laws, highlighting their performance relative to the classical Harten-Lax-van Leer (HLL) schemes. The schemes under…
We propose novel less diffusive schemes for conservative one- and two-dimensional hyperbolic systems of nonlinear partial differential equations (PDEs). The main challenges in the development of accurate and robust numerical methods for the…
This work introduces a novel adaptive central-upwind scheme designed for simulating compressible flows with discontinuities in the flow field. The proposed approach offers significant improvements in computational efficiency over the…
We introduce a locally divergence-free local characteristic decomposition based path-conservative central-upwind (LCD-PCCU) scheme for ideal magnetohydrodynamics (MHD) equations. The proposed method is a low-dissipation extension of the…
Central-upwind (CU) schemes are Riemann-problem-solver-free finite-volume methods widely applied to a variety of hyperbolic systems of PDEs. Exact solutions of these systems typically satisfy certain bounds, and it is highly desirable or…
A series of third- and fifth-order hybrid compact least-squares central weighted essentially non-oscillatory schemes are proposed and applied to curvilinear structured grids for the finite volume method. In smooth regions, compact…
We introduce new adaptive schemes for the one- and two-dimensional hyperbolic systems of conservation laws. Our schemes are based on an adaption strategy recently introduced in [{\sc S. Chu, A. Kurganov, and I. Menshov}, Appl. Numer. Math.,…
Explicit non-oscillatory central difference schemes become excessively diffusive when applied to highly nonlinear advection problems where small time steps are necessary to maintain stability. Here, we present a correction to reduce such…
In this work we present new second order semi-discrete central schemes for systems of hyperbolic conservation laws on curvilinear grids. Our methods generalise the two-dimensional central-upwind schemes developed by Kurganov and Tadmor. In…
The central-upwind flux is a widely used numerical flux function for local conservation laws. It has been investigated by Kurganov and Polizzi (2009) for a specific nonlocal conservation law and can be derived from a fully-discrete…
We present a new high-resolution, non-oscillatory semi-discrete central-upwind scheme for one-dimensional two-layer shallow-water flows with friction and entrainment along channels with arbitrary cross sections and bottom topography. These…
Central finite difference schemes have long been avoided in the context of two-phase flows for the advection of the phase indicator function due to numerical overshoots and undershoots associated with their dispersion errors. We will show…
A high-frequency recovered fully discrete low-regularity integrator is constructed to approximate rough and possibly discontinuous solutions of the semilinear wave equation. The proposed method, with high-frequency recovery techniques, can…
We develop a new second-order flux globalization based path-conservative central-upwind (PCCU) scheme for rotating shallow water magnetohydrodynamic equations. The new scheme is designed not only to maintain the divergence-free constraint…
In this paper, we present a fully local second-order upwind scheme, applicable on generic meshes. This is done by hybridisation, which is achieved by introducing unknowns on each edge of the mesh. By doing so, fluxes only depend on values…
Minimizing computational cost is one of the major challenges in the modelling and numerical analysis of hydrodynamics, and one of the ways to achieve this is by the use of quadtree grids. In this paper, we present an adaptive scheme on…