Optimized Compact-Difference-Based Finite-Volume Schemes for Linear Wave Phenomena

Fourth‐order compact schemes for solving multidimensional heat problems with Neumann boundary conditions

“…What makes these two sets of schemes different from many others, such as those reported in [2] and [3][4][5][6][7][8][9][10][11][12][13][14], is that they are uniformly fourth-order at both interior and boundary points. The LOD method is used so that the schemes are constructed through a sequence of two or three one-dimensional equations.…”

A Detailed Examination of the Finite-Volume, Time-Domain Method for Maxwell's Equations

“…An alternative to explicit differencing is implicit differencing, or compact differencing. For example, consider the following central compact operator [12,13]:…”

“…The manifestations of these errors, usually couched in terms of dissipation and dispersion errors, are best characterized in the frequency domain. Since such an analysis has been provided in many sources, we only note that the predominant error mechanism is dissipation [12]. One final note: Even though upwind schemes are well known to prevent grid decoupling, grid decoupling can be induced via the RungeKutta integrator.…”

Recent Advances in DNS and LES. Proceedings of the Second AFOSR International Conference on DNS and LES Held at Rutgers - The State University of New Jersey, New Brunswick, New Jersey on June 7-9, 1999

“…Its high-order features have shown great savings in both the memory and the time required to simulate highly curvilinear, realistic aerospace systems (Gaitonde and Shang, 1997;Gaitonde and Visbal, 1999). The extension of FDL3DI to handle the DNS of turbulent combustion systems must include the solution of the transport equations for the reacting species and the use of modern parallel computers because of the large number of equations and the stringent resolution requirements of reacting flows.…”