ward [3]) and ENO (Harten and Osher [4]) schemes. Later in the decade, Engquist et al. [5] proposed yet another method of For wave propagation problems in linear and bilinear elastic solids and a class of simple nonlinear solids the benefits of high-resolution introducing the required amount of dissipation, namely, the use schemes in gasdynamics can be immediately extended to solid of nonlinear filters. The advantage of these filters is that they mechanics. The Engquist filter for the system of conservation laws can be implemented into existing finite-difference codes. These in gasdynamics is extended to solid mechanics and implemented filters can be constructed to satisfy any set of criteria required in a finite-difference code. The present results show that highly by the high-resolution schemes. For example, the filter can be resolved numerical solutions, i.e., sharp shocks with very little oscillation behind them, can be achieved by applying this nonlinear constructed to satisfy the monotonicity preserving requirement filter to the finite-difference solution at every timestep. Plane wave of the TVD scheme, or it can be constructed to satisfy the propagation in three types of solids is calculated by the LAYER code. criteria leading to ENO schemes [6]. Using these filters, the A two-dimensional grid is used to compute these one-dimensional properties of the high-resolution schemes can be implemented plane wave problems. For linear elastic solids the nonlinear filter into a finite-difference code allowing the analyst to choose the performed very well in removing the Gibbs oscillations. For bilinear solids the numerical solution is compared to a known analytical best numerical approach for a given problem. This is a better solution. Because this analytical solution involves a planar shock investment than having to develop a new set of codes that uses with a decaying pressure behind it, the existing form of the Engquist the individual schemes. Moreover, the computing cost of these filter (designed for a constant pressure behind the shock) has to be newer schemes is at least a factor of several higher than finite modified. The relationship between this modified filter and the flux difference schemes. The main reason for the higher cost is modification in the TVD scheme is discussed. This modification is expected to be necessary when the filter is applied to multi-the characteristic decomposition [7], the Riemann solver or dimensional problems. The potential for obtaining highly resolved approximate Riemann solver [8], and the high-order fits to the shocks from classical second-order finite-difference solid mechanics solution. For some problems, the advanced schemes can be an codes using the modified nonlinear filter is demonstrated. แฎ 1996 order of magnitude more costly. The advantage of the filter, in Academic Press, Inc.
this case, is that typically only a relatively small number of grid points need be modified by the filter, resulting in substantial savings in computer time.
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