What Does TVD Stand For?

TVD stands for Total Variation Diminishing

Total Variation Diminishing (TVD) refers to a property of numerical schemes used in solving partial differential equations, particularly in the context of fluid dynamics and hyperbolic equations. A TVD scheme ensures that the total variation of the numerical solution does not increase over time, thereby preventing oscillations and maintaining solution stability. This property is crucial for accurately capturing sharp gradients and discontinuities in the solution while preserving physical fidelity. TVD methods are commonly employed in computational fluid dynamics and other areas requiring high-resolution simulations.