updates on benchmarks readme files

Author: hamidrezanorouzi

benchmarks/helicalMixer/readme.md

@@ -4,6 +4,12 @@
 
 This benchmark compares the performance of phasicFlow with a well-stablished commercial DEM software for simulating a helical mixer with varying particle counts (250k to 4M particles). The benchmark measures both computational efficiency and memory usage across different hardware configurations.
 
+**Summary of Results:**
+
+- phasicFlow achieves similar performance to the commercial DEM software on the same hardware.
+- phasicFlow shows a 30% performance improvement when using the NVIDIA RTX A4000 compared to the RTX 4050Ti.
+- Memory usage is approximately 50% lower in phasicFlow compared to the commercial software, with phasicFlow using about 0.7 GB of memory per million particles, while the commercial software uses about 1.5 GB per million particles.
+
 ## Simulation Setup
 
 <div align="center">

benchmarks/readme.md

@@ -1,7 +1,9 @@
 
 # Benchmarks
 
-Benchmakrs has been done on two different simulations: a simulation with simple geometry (rotating drum) and a simulation with complex geometry (helical mixer).
+Benchmakrs has been done on two different simulations: simulation with simple geometry (rotating drum) and a simulation with complex geometry (helical mixer). These benchmarks are used to show how PhasicFlow performs in different scenarios.
 
-- [rotating drum](./rotatingDrum/readme.md)
-- [helical mixer](./helicalMixer/readme.md)
+- [rotating drum](./rotatingDrum/)
+- [helical mixer](./helicalMixer/)
+
+**Note:** If you have performed benchmarks with PhasicFlow using other hardware or software other than PhasicFlow, we would be happy to include them in this section. Please open an issue for more arrangements or send a pull request with the benchmarks results.

benchmarks/rotatingDrum/readme.md

@@ -4,6 +4,12 @@
 
 This benchmark compares the performance of phasicFlow with a well-stablished commercial DEM software for simulating a rotating drum with varying particle counts (250k to 8M particles). The benchmark measures both computational efficiency and memory usage across different hardware configurations.
 
+**Summary of Results:**
+
+- phasicFlow achieves approximately 20% faster calculation than the commercial DEM software on the same hardware.
+- phasicFlow shows a 30% performance improvement when using the NVIDIA RTX A4000 compared to the RTX 4050Ti.
+- Memory usage is approximately 42% lower in phasicFlow compared to the commercial software, with phasicFlow using about 0.7 GB of memory per million particles, while the commercial software uses about 1.2 GB per million particles
+
 ## Simulation Setup
 
 <div align="center">