A high‐order Runge‐Kutta discontinuous Galerkin method with a subcell limiter on adaptive unstructured grids for two‐dimensional compressible inviscid flows
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DOI: 10.1002/fld.4757
Abstract: A robust, adaptive unstructured mesh refinement strategy for high‐order Runge‐Kutta discontinuous Galerkin method is proposed. The present work mainly focuses on accurate capturing of sharp gradient flow features like strong shocks in the simulations of… read more here.
Keywords: adaptive unstructured; order runge; inviscid; kutta discontinuous ... See more keywords
A Runge‐Kutta–based WENO reconstruction on moving mesh for compressible fluids
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DOI: 10.1002/fld.4775
Abstract: In this paper, we construct a high‐order moving mesh method based on total variation diminishing Runge‐Kutta and weighted essential nonoscillatory reconstruction for compressible fluid system. Beginning with the integral form of fluid system, we get… read more here.
Keywords: kutta based; moving mesh; based weno; reconstruction ... See more keywords
Explicit two‐step Runge‐Kutta methods for computational fluid dynamics solvers
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DOI: 10.1002/fld.4890
Abstract: Computational fluid dynamics (CFD) has emerged as a successful tool for industry applications and basic science during the last decades. However, accurate solutions involving vortex propagation, and separated and turbulent flows, are still associated with… read more here.
Keywords: runge; runge kutta; two step; fluid dynamics ... See more keywords
General order conditions for stochastic partitioned Runge–Kutta methods
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DOI: 10.1007/s10543-017-0693-6
Abstract: In this paper stochastic partitioned Runge–Kutta (SPRK) methods are considered. A general order theory for SPRK methods based on stochastic B-series and multicolored, multishaped rooted trees is developed. The theory is applied to prove the… read more here.
Keywords: partitioned runge; general order; stochastic partitioned; order ... See more keywords
New stability results for explicit Runge–Kutta methods
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DOI: 10.1007/s10543-019-00752-9
Abstract: The theory of polar forms of polynomials is used to provide sharp bounds on the radius of the largest possible disc (absolute stability radius), and on the length of the largest possible real interval (parabolic… read more here.
Keywords: explicit runge; stability radius; new stability; absolute stability ... See more keywords
Efficient exponential Runge–Kutta methods of high order: construction and implementation
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DOI: 10.1007/s10543-020-00834-z
Abstract: Exponential Runge–Kutta methods have shown to be competitive for the time integration of stiff semilinear parabolic PDEs. The current construction of stiffly accurate exponential Runge–Kutta methods, however, relies on a convergence result that requires weakening… read more here.
Keywords: kutta methods; order; exponential runge; runge kutta ... See more keywords
A new embedded 4(3) pair of modified two-derivative Runge–Kutta methods with FSAL property for the numerical solution of the Schrödinger equation
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DOI: 10.1007/s10910-018-0974-6
Abstract: A new embedded 4(3) pair of modified two-derivative Runge–Kutta (TDRK) methods with First Same As Last (FSAL) property for the numerical solution of the Schrödinger equation is constructed in this paper. Both the error analysis… read more here.
Keywords: embedded pair; pair; runge kutta; new embedded ... See more keywords
Simulating Compressible Two-Medium Flows with Sharp-Interface Adaptive Runge–Kutta Discontinuous Galerkin Methods
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DOI: 10.1007/s10915-017-0511-y
Abstract: A cut cell based sharp-interface Runge–Kutta discontinuous Galerkin method, with quadtree-like adaptive mesh refinement, is developed for simulating compressible two-medium flows with clear interfaces. In this approach, the free interface is represented by curved cut… read more here.
Keywords: sharp interface; medium; discontinuous galerkin; runge kutta ... See more keywords
New Integration Methods for Perturbed ODEs Based on Symplectic Implicit Runge–Kutta Schemes with Application to Solar System Simulations
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DOI: 10.1007/s10915-017-0634-1
Abstract: We propose a family of integrators, flow-composed implicit Runge–Kutta methods, for perturbations of nonlinear ordinary differential equations, consisting of the composition of flows of the unperturbed part alternated with one step of an implicit Runge–Kutta… read more here.
Keywords: solar system; system; implicit runge; runge kutta ... See more keywords
Optimal Monotonicity-Preserving Perturbations of a Given Runge–Kutta Method
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DOI: 10.1007/s10915-018-0664-3
Abstract: Perturbed Runge–Kutta methods (also referred to as downwind Runge–Kutta methods) can guarantee monotonicity preservation under larger step sizes relative to their traditional Runge–Kutta counterparts. In this paper we study the question of how to optimally… read more here.
Keywords: monotonicity; perturbations given; preserving perturbations; runge kutta ... See more keywords
A Compact Subcell WENO Limiting Strategy Using Immediate Neighbors for Runge-Kutta Discontinuous Galerkin Methods for Unstructured Meshes
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DOI: 10.1007/s10915-021-01725-3
Abstract: In this paper, we generalize the compact subcell weighted essentially non oscillatory (CSWENO) limiting strategy for Runge-Kutta discontinuous Galerkin method developed recently in [ 1 ] for structured meshes to unstructured triangular meshes. The main… read more here.
Keywords: discontinuous galerkin; limiting strategy; strategy; kutta discontinuous ... See more keywords