Deltaic systems are vulnerable landscapes and stratigraphic archives, but modeling their evolution over long timescales requires methods that conserve sediment while allowing geomorphic boundaries to move. We present GeoEnthalpy-Delta v1.0, a fixed-grid enthalpy model for idealized fluvial-deltaic evolution in one and two spatial dimensions. The model evolves sediment thickness over a prescribed non-erodible basement, reconstructs the sediment surface, and diagnoses the alluvial–bedrock transition, shoreline, and delta toe from the evolving thickness and surface-elevation fields. Sediment redistribution is represented by a thresholded, slope-driven transport law with separate topset, foreset, down-system, and lateral mobility parameters, allowing finite foreset storage and fan-delta planform spreading without remeshing or explicit front tracking.</p> <p>We verify the one-dimensional implementation against analytical benchmarks for fixed sea level, square-root sea-level histories, vertical-foreset and graded-river limits, and post-autobreak retreat under constant sea-level rise. Two-dimensional experiments are evaluated using mass conservation, grid consistency, and moving-boundary diagnostics. Model demonstrations show that shoreline retreat can occur while the toe continues to prograde during cyclic sea-level forcing, and that lateral thresholds, foreset thresholds, sediment input, and feeder width control fan width, shoreline-to-toe separation, and sediment partitioning. GeoEnthalpy-Delta v1.0 provides a compact and reproducible baseline for studying coupled delta morphology and stratigraphy and for future incorporation of hydrodynamic, coastal, and subsidence processes.