Numerical Methods in Fluid Dynamics

finite difference method hyperbolic conservation laws parabolic equations finite difference approximation irregular boundaries stability of the solution accuracy of finite difference approximations initial boundary- value problems Lax's theorem linear parabolic equation in a one space dimension numerical fluid dynamics

Mathematics Subject Classification ID

Navier-Stokes equations (35Q30) Research exposition (monographs, survey articles) pertaining to fluid mechanics (76-02) Basic methods in fluid mechanics (76M99) Incompressible viscous fluids (76Dxx)

Related Items (51)

A numerical study of oxygen diffusion in a spherical cell with the Michaelis-Menten oxygen uptake kinetics ⋮ Numerical solution of structured population models. II: Mass structure ⋮ An alternating direction implicit method for a second-order hyperbolic diffusion equation with convection ⋮ A method of differential iteration for boundary value problems in extended thermodynamics ⋮ Selected topics in the theory and practice of computational fluid dynamics ⋮ Development of a Godunov method for Maxwell's equations with adaptive mesh refinement ⋮ Shortening three-dimensional curves via two-dimensional flows ⋮ A dictionary approach to reaction-diffusion systems with nonlinear diffusion coefficients ⋮ Construction of modified Godunov-type schemes accurate at any Mach number for the compressible Euler system ⋮ A generalized alternating-direction implicit scheme for incompressible magnetohydrodynamic viscous flows at low magnetic Reynolds number ⋮ A visual fluctuation splitting scheme for magnetohydrodynamics with a new sonic fix and Euler limit ⋮ Nonlinear Hyperbolic Systems of Conservation Laws and Related Applications ⋮ A highly efficient finite volume method with a diffusion control parameter for hyperbolic problems ⋮ On the condition number of a Kreiss matrix ⋮ On stationary solutions to plane Broadwell model ⋮ Effect of moving boundaries on the vibrating elastic string. ⋮ The numerical and analytical solution of ill-posed systems of conservation laws ⋮ A new shock-capturing technique based on moving least squares for higher-order numerical schemes on unstructured grids ⋮ On a conjecture by LeVeque and Trefethen related to the Kreiss matrix theorem ⋮ Numerical simulation of flame propagations in circular cylinders ⋮ Dynamical approach study of spurious steady-state numerical solutions of nonlinear differential equations. I: The dynamics of time discretization and its implications for algorithm development in computational fluid dynamics ⋮ A symplectic algorithm for wave equations ⋮ Towards an Accurate and Robust Roe-Type Scheme for All Mach Number Flows ⋮ A phenomenon of artificial odd-even grid oscillation and its presence in domain decomposition computation: algebraic analysis and numerical illustration ⋮ An interface tracking method for hyperbolic systems of conservation laws ⋮ A local space-time conservation scheme and its application in shock wave propagation ⋮ Characteristic evolution and matching ⋮ Stability analysis of the Euler-Poisson equations ⋮ Numerical solution of structured population models. I: Age structure ⋮ Characteristic evolution and matching ⋮ Instability of cooperative adaptive cruise control traffic flow: a macroscopic approach ⋮ Three snippets of curve evolution theory in computer vision ⋮ A review and comparative study of upwind biased schemes for compressible flow computation. II: 1-D higher-order schemes ⋮ A review and comparative study of upwing biased schemes for compressible flow computation. I: 1-D first-order schemes ⋮ Characteristic evolution and matching ⋮ Central finite volume methods with constrained transport divergence treatment for ideal MHD ⋮ Accurate Boundary Conditions for Exterior Problems in Gas Dynamics ⋮ Adaptive reconnection-based arbitrary Lagrangian Eulerian method ⋮ Performance of some finite difference methods for a 3D advection-diffusion equation ⋮ TVD schemes for the calculation of flow in pipes of variable cross- section ⋮ Spherical symmetric parabolic dust collapse: 𝒞1 matching metric with zero intrinsic energy ⋮ Capturing material interfaces ⋮ A review and comparative study of upwind biased schemes for compressible flow computation. III: Multidimensional extension on unstructured grids. ⋮ Conformal curvature flows: from phase transitions to active vision ⋮ Numerical solution of nonlinear hyperbolic conservation laws using exponential splines ⋮ Characteristic evolution and matching ⋮ Characteristic evolution and matching ⋮ A study of finite amplitude plane wave propagation in a rubber-like solid ⋮ A numerical study of the Riemann solutions for gasdynamic combustion ⋮ High order finite difference schemes with application to wave propagation problems ⋮ The stiff conservation laws and the MacCormack difference scheme

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